The car turns off in drive and stutters?

I'm not super knowledgeable about cars. I'm trying to learn but out of nowhere the car suddenly started having a problem. At first it felt like the car was stuck in 2nd and 1st gear, if I pressed on the gas the RPMs would go up, but I couldn't accelerate past 60km and then the RPMs started stuttering or jumping and the engine would shake heavily when that happened. Then as I was waiting to turn to take it home it shut off, the engine shut off in drive and wouldn't start again, I had to run out and boost it and it started immediately. I took it home and left it overnight, went out to try and start it and it would turn over multiple times but not start for a while, it did eventually and in park idled but after 10 minutes started stuttering again, neutral was the same, but then I put in in drive and it almost immediately shut off. My dad suggested it might be that there's a problem going to the computer because the first time it turned off all the lights stayed on and my music, yet it still needed a boost to start and showed the battery light. The battery is relatively new. And alternator is about a month old.