Have I got a sensitive tooth or is something wrong with it?

So I'm 13 and never had a sensitive tooth before. I know o have some gum problems and at least 2 cavities. I haven't seen a dentist in years but I know as my gums bleed ect. This morning I suddenly had a glass of cold water and this pain came into my tooth (like when u bite into ice Lolita with your front teeth) then went away like a second later. It's on the same tooth as the one with the cavity on