Hey I just realized that the back of my tongue is touching my uvula and pushing it back into my mouth. Am I doing something wrong?
No, thats actually okay. The uvula is in the back of the mouth, connected to the soft palate, which should also be in contact with the tongue. So being aware of the sensation/touch between the uvula/tonsils/soft palate and the back of your tongue is a good feedback.
Not very good would be if your gag reflex were activated the whole time, but I doubt that's your case.