One company reimbursed my medicare and social security taxes because I earned less than $2,600. Another company hasn't reimbursed me, do I get it back on federal taxes?

Don't know why that company is reimbursing you for SS and Medicare.  No you don't get those back.  Only federal income tax withheld box 2 and state tax withheld in box 17.

Are you a US Citizen or Resident?  If not, then you need to file form 8316 to request a refund and Sprintax.com to file your tax return as TurboTax does not handle non-resident returns. 

If you are a US Citizen or Resident, in general, you should not get your SS and Medicare back if you made only $2,600.  If for some reason you overpaid in to Medicare and SS, you would not get them back on your federal refund.  You would need to file form 843 to request a refund of the amounts withheld that should not have been withheld.