I have a Core 15 that I bought 4-5 years ago, second hand from a guy that never fired it. Only thing I changed was the stock from a collapsible to fixed, because of my sate's laws, so now it has a rifle length buffer and spring.

Two range sessions ago my rifle was acting up. It was failing to feed. Sometimes it would fire, eject the spent round and go back into battery without picking up the next round. I took it home cleaned it real good and checked the gas block (when I first got the rifle the gas block was loose causing short stroking) I had it happen in past range sessions, but seemed to clear up when I stopped using certain magazines and I stayed using my Magpul ones. I was using .223 of various manufacture.

At mt last session I used 5.56 to see if the added pressure would fix it, but it was acting up again with all my magazines. I would fire 2 rounds and then it would fail to feed. Most of the time not picking up a round at all. I would pull the charging handle and get another 2-3 rounds before it would do it again. Then it did it again, but this time I couldn't pull the charging handle at all. It was stuck.

I took it home and tapped the charging handle with a rubber mallet and go it to eject. I tried running clean rounds into the chamber after I got it cleared and none of them would go in to full battery. The round would eject, but I had to pull real hard.
I later took to friend and tried the spent case that got stuck in mine, in his M&P and it went in and out flawlessly. I also tried my BCG in his upper and it worked fine. I tried his BCG in my upper and the case would get stuck in the chamber.

I have come to the conclusion it's a bad barrel, but before I throw money at the problem and find out it didn't fix it. I want to hear what some more experienced people have to say.

I really doubt it's a bad barrel. They don't go bad like that. When is the last time you cleaned it or cleaned the chamber? Have you lubed it?

I cleaned the chamber with a chamber brush and solvent before my last range session.
I lubed it at the same time. I didn't specifically lube the chamber, but i did run a lubed patch through the barrel.

I really don't think it's the barrel unless it's always been like that or became really corroded.  Did it function fine before? What's the approximate round count?
 I've seen new ARs do it just needing broken in and  I have seen dirty chambers make it harder to extract but never a chamber that just went bad.
So you are saying the round is getting stuck in the chamber? And is unable to be extracted out? I just want to verify I'm reading it correctly. Is the extractor gripping the round?

The round went in just fine. After I fired, it was stuck and I couldn't eject it by pulling on the charging handle. I had to tap the charging handle with a mallet to get it to eject, so yes, it was extracted by the bolt.

As far as round count, just shy of 1500.

Every time I've taken it to the range I've had at least one failure to feed issue. I always blamed it on a couple of the magazines I have, to the point I rebuilt the magazines with anti tilt followers and they didn't help. This whole issue now makes me think the short stroking/failure to feed was caused by the resistance of the empty case being stuck in the chamber while it was trying to extract and not having enough energy to push the BCG back far enough to properly pick up the next round.

After I got home I did a test with the stuck casing that I had removed. I dropped it in a friends AR and in went into the chamber and the bolt went into full battery and then extracted without a problem. I then tried the same thing on mine and it wouldn't go into full battery and I had to tap the charging handle to get it to extract. This makes me think there is an issue with the chamber on my AR.

Could be that some corrosive ammunition ate up your chamber or extension and deformed it. Maybe didn't get cleaned well enough? What do the spent cases look like? Any odd rub marks on the bolt lugs?

I think you have an ammunition problem, not a rifle problem. BTW-Western nations stopped using corrosive ammunition in the early 1950's.

You haven't stated what ammo you are using, only referring to it as 5.56mm.

I never shoot steel case in my .223 rifles, some have reported crud build up in the chambers from the coating some companies apply, others a short barrel life because the bullets are usually made of copper "washed" mild steel. Use a bronze bristle brush and solvent to remove any built-up crud in the barrel's throat.

Headpsace gets longer over time, so there is no way your barrel chamber is too tight after 1500 rounds downrange. Your ammunition shoulder is too tall, causing it to bind in the chamber when the bolt goes home. If you reload, the sizing die needs to be screwed down more. This is the only way to create this problem on a rifle that worked fine for 1500 rounds.

If it’s jammed every time you shot it for 1500 rounds them you have a problem.  Gage the chamber.

ARs don’t typically malfunction.

For example:  My main range beater (16” carbine Colt, let the hipsters choke on a dick) is on it’s second barrel, has over 20K rounds through it, and has never, not even once, failed to fire, feed, extract, eject, or lock back.

I've been using a mix of various manufactures for ammo, but no steel cases and no reloads. I've been mostly using 55 grain .223, because that what I have the most of.
I used all 5.56 at the last range session to run a test and see if the rifle performed better with the higher pressures.

An update on where I stand with this issue.

I gauged it with a Go and NoGo gauge and it was fine.

I then decided to look at the ammo I was using by cycling a full magazine of each manufacture, by hand. And to help explain my findings for this I'll use a scale of 1-5. 1 being no resistance while cycling and 5 being stuck in the chamber. The ammo I test was Winchester 5.56, Norma 2.23 and some Turkish ammo in 5.56 all 55 grain.

The Winchester, I give it a 1 on my scale. It cycled fine with no hang ups
The Norma, I give a 2.5 on my scale. 2 or 3 would cycle fine and then I would get one that I would have to pull real hard to get it to eject.
The Turkish ammo, I give a 4 on my scale. Everyone was very hard to cycle and a few got stuck and I need to tap the charging handle to get it to eject.

That tells me there is something up with the different ammo in my gun, but at my last range session I had my buddy test one of my questionable magazines in his gun and I gave it to him loaded with the Turkish ammo and it fired flawlessly through his gun.
I wasn't real sure what to do. Do I just shoot Winchester ammo and hope one day the chamber wears out a little so I can shoot other manufacture's ammo.
What I did do was buy a complete Del-Ton upper and ran my test again with with the same ammo and the result were that all 3 manufactures ammo cycled with out issue. I give them all a 1 on my scale.

My next step is to take it to the range and fire it, that will be the true test.

This sounds like a roughly finished chamber on the tight side with some hard fouling and/or dried preservative grease. I've used a .30 caliber bore mop with some Blue Magic Metal Polish Cream (available at auto parts stores) on it in a cleaning rod section chucked in a drill set on low speed to clean stubborn dirt from .223 chambers. A couple minutes running the mop in and out (of the chamber) should have everything cleaned out and lightly polished. A .40 caliber mop works well on .308 Winchester chambers.

2.23 caliber Norma ammo? That must have a bit of a kick to it.

Does the bolt lock back on the last round?