If you did not deduct the contribution and you do not want to anend then you are required to file a 8606 form showing the non-deductible contribution on line 1, the total of any previous non-deductible contributions on line 2, the total of lines 1 & 2 on line 3 and 14.   That 8606 must be mailed to the IRS.    There is a $50 penalty for failing to file the 8606.

Hopefully, you had enough earned compensation to make the contribution.  Even if your parents make it, you must have at least that amount of earned income or it is an excess contribution subject to a 6% penalty each year that it remains in the account.

You can either amend and claim the contribution as a deductible contribution, or download and mail the 2015 8606.

Prior year form can be downloaded here - enter 8606 in the find box.   The instructions are there also.
https://apps.irs.gov/app/picklist/list/priorFormPublication.html

If I do amend, then does that mean I don't need to fill out  8606? And will I still be charged a penalty? I'm not sure what the recommended route would be - to amend or not amend.

I don't see a line for Roth IRA anywhere on the actual return page, but I have a worksheet attached to my return and that indicates I contributed to Roth. If it turns out I didn't contribute to roth and the money was actually contributed to a traditional, what would you recommend? Thanks!

If you amend and claim the deduction you do not need the 8606.   If you had earned income in 2015, there will be no penalty.   You will probably get a refund if you had a tax liability.  Entering the Traditional IRA contribution in the amended return will tell you.

You won't find a Roth anywhere since a Roth is after-tax money so it does not get reported on a tax return, only Traditional IRA's must be reported - either as a before-tax deduction or an after-tax basis on a 8606 form that won't be taxed again when it is distributed.

Enter IRA contributions here:
Federal Taxes,
Deductions & Credits,
I’ll choose what I work on (if that screen comes up),
Retirement & Investments,
Traditional & Roth IRA contribution.

OR  Use the "Tools" menu  (if online version under My Account) and then "Search Topics" for "ira contributions" which will take you to the same place.

For reason to amend simply say something like "forgot to include Traditional IRA deduction" ... there won't be a problem. But see how much money you save. It might or might not be worth it. That is your call.

Thank you I just found out this morning that the contributions were, in fact, traditional.

My parents had made contributions under my name since 2012. Now I'm going to look into whether they claimed the contribution on their return in 2012 and I'm still looking for a copy of 2013.

Will I be able to amend 2012 return or what do you suggest? Every year they contributed $5500. I'm trying to see how I can fix all of this and I'm so lost...

Could the account the funds are in, be transferred to a Roth IRA instead?  That is apparently how the return appears to have been filed.  They would be "fixing" the account to match what was reported to the IRS.