The last few times I have worn lipstick I got lots of coldsores the day after, is there any that wouldn't cause this? What is it in the lipstick that would have this reaction?

I have really sensitive skin, too.
There is a lip gloss by L'Oreal that absolutely made my lips inflate the size of balloons.
Try to use more natural products and test a few out, with just a small amount on your lips.

Maybe they were not "coldsores" but the reaction to something like lanolin in the lipstick.

Or maybe it was an old lipstick and got bacteria on it?

Toss all makeup that is over 3 months old unless you keep it in the fridge. Yes, makeup can develop bacteria just as anything else can.

Learn to be a label reader!! If in doubt of whether something is an "allergen" to you or not, test it in the bend of the elbow 24 hours before purchasing it. That is one of the most sensitive spots on the bod and if it turns red, rashy, splotchy, don't use that product.