Employer withheld too much ss and medicare tax, can I go ahead and fix the amount myself in turbotax, and file them, and then request a refund from my employer on a later date?

How do you know?  Did Turbo Tax say he did?  It might just be for SS.  There is no max on Medicare.

Check boxes 3 & 4 on your W2. Box 4 should be 6.2% of box 3 up to a max of $8,239.80.   So take the amount in box 3 and multiply it by .062. If box 4 is more than that you need to get a corrected W2 from your employer.  But also go back and double check your W2 entries, you may have entered box 3 & 4 wrong.  A lot of people who have asked this found they did enter an amount wrong.

Or check W2 box 12.  You may have entered Code A by mistake.

A sure way to fix this is to delete the W2 and re-enter it.  That may clear something out.

Or post back with the amounts in boxes 3&4.