The clutch packs are probably worn out. If it is manual or automatic, it still has a set of clutch packs. Although on an automatic there are a few other variables. The torque converter could be bad, the torque converter clutch solenoid or it might not be shifting exactly into gear. The shifter has to put the transmission exactly in the detent for the gear. If it does not it can cause problems like you are having and lead to a rebuild.
I suggest you take your car to a Transmission shop. Not a regular repair facility as automatics are hard to diagnose and require special tools to fix. AAMCO is overpriced, so don't go there. Use the search engine on this site to find a transmission shop bnear you.