Child has 1 blister on her throat and was exposed to strep. Could strep cause a blister and slightly red throat?

Maybe. Blisters are usually on the skin, and what you are describing may be exudates, viral or bacterial. With the recent exposure to strep, a throat culture is advisable, and this can be done at either the pcp or the otolaryngologist.
Yes. See a doctor to get a throat culture. Then you'll know if antibiotics sre needed.
Go to your pcp. You should go to your pcp to run some tests such as a step test to confirm it is due to strep.