1999 Chevy Monte Carlo Would this be a transmission issue?

I just recently had to replace my alternator when I was out of town this past weekend. I made the three hour trip back home after the fix and had no other issues with my car. The next day, I went to visit a friend after work and stopped to get gas after said visit. Once I was finished I put my car into drive to leave the gas station, but the car wouldn't move -- it was as though my car was still in park and I was revving the engine. I eventually gave it some more gas and I heard a loud knock/bang noise, then the car started moving forward just fine. The following morning I had the same issue, but when I gave the car some extra gas, the car would drag forward slowly like one of my tires wouldn't move (it kind of felt like a flat but worse and I also heard the sound of one of the tires dragging). I got out of the car to look at my tires, they were fine, and then I put my car into reverse -- the car moved back just fine and when I put it back into drive, the car started moving forward again like it was suppose to. I decided to test it again when I had to park for a doctor's appointment that same day. I made sure I was parked where I would have to go forward instead of backwards (don't seem to have any reverse issues). Sure enough, when I put my car into drive I had to give it some extra gas, I heard that noise again, and then the car would go forward no problem. I have also noticed that my car feels like it has a lame leg when I was on the highway (noticeable friction?) -- My gas consumption is also noticeably higher. Would this be a transmission issue or is it possible that there is something wrong with my axles/tires/etc?