UHM...HELP! 01 Sunfire shifting problems!

We have a 01 sunfire that stopped running. I have a feeling that the mechanics just made stuff up and after several hundreds of dollars we brought it home. They changed the altenator, 2 solanoids (all for a check engine light) then said it needed a new fuel pump. The original problem was a dying issue...hence the altenator. We brought it home, not running and changed the fuel pump ourselves. Now, it runs but revs up to 6000 rpms before shifting from 2nd to 3rd. It will shift if we manually shift from 1, 2, to D. It's like the overdrive isn't working or something but I have no idea where to look and hesitate to take it back to the mechanic (of course we could get a new one) but I'd like to have some idea before they just randomly start telling me things I need to fix...i.e., I'm sure the problem was the fuel pump all along and NOT THE altenator - oh and when I suggested the battery they told me the battery was fine - of course it's not, it won't hold a charge and needs to be replaced...

Any ideas I would LOVE to hear - any general directions - ANYTHING!!