It sounds like the shift levers and cable tension needs adjusting.

It is hard to guess without seeing it. If it is teeth wear and chain stretch, the damage is done together chain to teeth so that you don't usually notice the problem until you try to put on a new chain or sprocket. I suspect something else is going on.

Check shift lever and cable tension.

No chance that the front derailure is hitting the chain? Check that too.

Surely your wheel is centered correctly so the chain isn't trying to climb on the sprocket at an angle? Check that too.

Mike