If you have not received confirmation through TurboTax that your returns were submitted, you would need to log back into your account to be sure it was not rejected. It is possible that any emails telling you that the return was submitted, accepted or rejected could be in your spam mail.
You can also go to the IRS website for Where's My Refund to track the status of your return.
Since you are on a J-1 Visa, have you met the substantial presence test to be treated as a US Resident for tax purposes? If you have not, met the substantial presence test and are considered a Non-Resident Alien, then you would need to file a 1040-NR instead of a form 1040. If you have filed the 1040, but should have filed the 1040-NR, you could use Sprintax.com to help with getting the proper forms filed and the correction made.