1995 Pontiac Grand Am Would this be a transmission problem?

We recently had our alignment done, which we found do be worse than it was before. Then the care would not go in reverse right away, we would have to put it in neutral then pop it into reverse. Now it doesn't want to go into drive as well. We took it back to Firestone and told them the alignment was messed up worse than before and that now we're experiencing the car not going into gear. He said it's a transmission problem. My husband said he thinks they might have messed something up with the drive shaft (although that's not the exact part he said) but it's something along those lines.

What do you think?