Sounds like a linkage problem. Usually, if you're shifting into gears, a tranny problem would be if you couldn't back out of say..., a parking space and you suddenly found you had no reverse. Or you're at a stop sign, step on the gas and you're not moving although you're in D.
Go ahead and check your fluids.
I had a problem corrected where I'd put the Vette in park and it wanted to keep going backwards or forward, depending on the level of the street. I had to use the park brake to make sure it wouldn't move. Good thing I noticed it before I hit the gas for revs while parked in front of someone!!!
Turns out a bolt had fallen completely out of the shifter control cable where it attaches to the transmission. It was about a 40 minute fix.
Hope this helps.