Chain skipping on upper pulley of rear derailleur
New chains are not sized out of the box (i.e. they are usually several links too long). Part of installing a new chain is to size it by removing links prior to installing it to match the length of the old chain.
I suspect you may have mis-sized the chain. Otherwise it is possible that your jockey wheel on the derailleur is worn. Those can also be replaced individually.
I am not expert on sizing a chain, but Calvin is so here you go:

                
            
Also, no shame in going to a LBS to have them look at the drivetrain, size the chain, adjust the B screw as they do it day in and day out plus it requires a few special tools. You probably could get all of that fixed up for $20-$30 plus parts if any are required.
Hope that helps.