I replaced my radiator about 5,000 miles ago, and I've noticed my car getting hot again. Before, I replaced a faulty water pump and radiator after hearing a leak on the old radiator. Anyway, its doing the getting hot then going back to normal, then hot again, as if there may be air in there, but I'll check the coolant levels and its low in the radiator itself, but there will still be coolant in the overflow. I thought head gasket first, but there isn't any smoke coming out, no steam, and no coolant in the oil for the head gasket symptoms, so I'm thinking maybe a leak in the coolant system. The thermostat was changed with the radiator, so I'm kind of ruling that out. Maybe the ECT, but I guess I need to pressure test the whole thing. I'm just confused about coolant not moving from the overflow. I pulled the hole and blew in it to see if there was an obstruction, and I got bubbles so that's good. Is it possible the new radiator (aftermarket) and old OEM radiator cap are not meshing and therefore I'm loosing pressure and vacuum? Water pump isn't leaking, and nor am I finding any coolant leaks anywhere.

Radiator caps are dirt cheap, replace it and see what happens.  An old leaky cap may have been preventing your system from pressurizing, or from pressurizing enough.  You may have a bad head gasket of course, you can actually get a head gasket test kit and find out if any exhaust gasses are making their way into your cooling system.  

Something like this:

http://www.amazon.com/Lisle-75500-Combustion-Leak-Detector/dp/B0007ZDRUI

ETA:  If you want to make sure you have no air in your system, park on a slight hill so that the radiator cap is the high point in the system, turn your heater on full hot, take the cap off, and let it come all the way up to temp.  When you see the coolant start to circulate as the thermostat opens and closes, top off the fluid and install the cap.

Year, make, model?
Was the coolant system bled of air correctly? Air pocket will cause an overheat as it stops the t stat from opening. Radiator cap is cheap. Also, does the t stat have a small bleed hole in it?

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Its a 2004 corolla. I still think there is air in the system because when I put some water in it today, bubbles came up.

If you are losing coolant, and there is no evidence of external leakage there is only one place for it to go, out your exhaust via a cracked head or bad head gasket.  I know you don't have white smoke, but that's not always present.  Have you pulled the spark plugs?  If one is very clean and shiny compared to the others that's because it is being steam cleaned by your head gasket leak.