Is there an std that causes a sore throat and gum pain?

Yep: Syphillis is one std that causes sores. They are called chancres. They can be located anywhere in the mouth. Go see a doctor and a round of antibiotics could clear up the whole problem. Just don't have any physical contact with anyone until you are cleared. Not a nice "gift" to give to others.

Another: Oral herpes can also cause lesions in the mouth.