I went to America with J1 student visa worked for 4 months as allowed. During that time my W-4 was entered incorrectly. First I was paying everything when I kept being told I shouldn't be paying social security. Weeks later I was able to get a hold of a form to refile the W-4 but I was instructed poorly because on next paycheck income tax wasn't taken and social security was. I worked in FL so no state or local taxes were taken. I was thinking I could file 1040NR-EZ but it comes up saying I owe money. Aren't I entitled to get back the Social Security tax that was withheld?

On J-1 (student) you are exempt from residency for 5-years. You must file non-resident tax return Form 1040NR or 1040NR-EZ and Form 8843. Your income is not subject to FICA taxes but you must pay federal and state income taxes.
On your income you will get deduction based on tax treaty between the U.S. and your country. Your U.S. Tax Return: U.S. Tax Filing Requirements for Non-Residents

Your refund of SS tax and Medicare tax, first you must ask your employer. Write them a letter or email. You can attach a copy of page 50-51 of IRS Publication 519: Tax for Aliens.  (Read Social Security and Medicare Tax-- Students and Exchange Visitors). If they are unable to refund you, you will file Form 843 with IRS. File form 843 after one month of filing your nonresident tax return. Your U.S. Tax Return: Social Security and Medicare (FICA) Taxes for Non-resident Exempt Individual

Thank you that is helpful. I'm from the UK. I can not contact my former employer. On form 843 it says see Pub. 519 for special instructions for Non Res Students.. That's what I am but I can't make any sense of what is on Pub 519.. Should I still just file the 1040NR-EZ and then wait a month to file Form 843?

You can file the Form 843 and 8316 at the same time as you file the Form 1040NR-EZ.

You just mail it in a separate envelope to a separate address (to Philadelphia, Pennsylvania).