This was a hand that was dealt to me yesterday. Tell me what you all think. I was playing 1/2 limit PP.

I'm in MP dealt 88. A few call to me and I just call. No one raises pre-flop. Flop is AAx. One bets and I'm the only caller. Turn is 8. I just hit a full boat, so I bet out and it ends up capped. I put him on Ax. River is J. I check, he bets, I call. He shows AJ for aces full of jacks. Was my betting and raising correct in this situation?