First of all, don't listen to the entire old wife's tales about matches, Vaseline, oil, etc... They are just that, wife's tales.
You should NEVER NEVER NEVER use anything hot to remove a tick. Heating that little bastard up will essentially pressurize his body, pushing all the nasty bacteria and disease into your body (or your dogs). Also, never squeeze them with your fingers for the exact reason. This is more of a concern with deer ticks since they carry lime disease, but rocky mountain fever is also transmitted this way.
Covering a tick with Vaseline is likely to suffocate it. Then you've got a dead tick embedded in your hairline.
If you break off their mouth parts by yanking them off, it might cause an infection, but will probably only cause irritation until your body takes care of it. It's sort of like having a tiny splinter at that point. Leaving any part of a tick in your body increases your risk of contracting a disease.
Most of the time, if you remove a tick within 24 hours you won't contract anything. What I'm saying is that if you're driving down the road and find a tick on your arm you don't have to stop and pull the sucker off. Wait until you can do it calmly and carefully, but don't wait more than a few hours.
Female ticks and nymphs enlarge up to 60 times their normal size when engorged on your blood.
The proper way to remove a tick is to get a tick tweezers, or some other small tweezers and grab them as close to the skin as possible. If you don't have a tick tweezers, you can improvise with a stiff playing card. Cut a very small wedge out of one end so that it comes to a very sharp point that points toward the center of the card. Work the card/wedge under the tick from it's back side so that its body is on top of the card and only its mouth (imbedded in your skin) is in the absolute point of the wedge. Now carefully, slowly pull the card up, keeping the ticks mouth in the wedge (use your hands, it won't hurt you) until you get it out. If you do it right, you'll have a complete tick on top of the card and nothing left in your skin. You don't want to push any fluids back into yourself after they've been in a tick. Now take that happy little blood sucker, set him carefully on the ground, and STOMP HIM UNTIL YOU ARE SATISFIED!!!
If your dog has a very large swollen spot where the tick was, it sounds like it might be infected. Especially if it is sensitive. If it's just a hard spot and it's not bothering the dog I wouldn't worry about it very much. Just keep an eye on it in case it gets worse. If it starts to ooze or anything I would definitely take him to a vet.
(edited because I can't spell)