I got a tooth filling a couple months ago and after a couple weeks later I stated feeling sensitivity around it and now it's going from the top and now even my bottom left gums are hurting, and when they start hurting, the left side of my throat starts to hurt. I have been doing excessive drinking so I don't know if it's my throat that is making the left side of my mouth hurting or is my my tooth that is making my throat hurting? Should I go to the dentist? Or should I go to the doctors for my throat?

Sounds like you have a seriouly impacted tooth and should go to the dentist immediately. Impacted infected roots on a tooth will effect your gums because the infection is building up and it is has no where to go. Better see your dentist before it gets any worse.

Definitely, tickle's right. Get to your dentist ASAP. (Can't greenie you tickle, I have to "spread my greenies around")