I originally just bought Morrowind (not GOTY edition) and made a character. Then a while later I got Bloodmoon. I was just wondering if I could use my already created character or if I had to make a new one to be able to play Bloodmoon.

Nope, I am pleased to inform you that you are good with the one you already created! Bloodmoon will be ready when you are, just talk to folks about "Latest Rumors"

Oh thank goodness!

Yep, you can keep playing with your character on Solstheim.

The same also applies with Tribunal.

Although it will "parse your Journal."

Tribunal updated the journal functions and it just takes a few seconds to update your save file.