Since you internship was a temporary assignment you can deduct your travel expenses if they otherwise qualify for deduction. You can deduct ordinary and necessary expenses you have when you travel away from home on business. The type of expense you can deduct depends on the facts and your circumstances. To determine what you can deduct see IRS PUB 463 Travel, Entertainment,
Gift and Car Expenses
Once you have determined what you can deduct you will deduct them as un-reimubursed business expenses. In order to take the deduction you will need to itemize your deductions.
As for the two states, you will need to file a non-resident return for the state where your internship was located. Your resident state will give you a credit for any tax you pay to your non resident state, so you won't be double taxed on that income.
