Can I file travel expenses for using my vehicle , working and living in two different states? If so how could I log that?

If you are not self-employed or otherwise not using the vehicle for a business, the vehicle and other travel expenses are not deductible on a federal tax return.

It depends.  If you are a W-2 employee, no. Commuting miles are the miles you drive between your home and your regular place of employment.  Commuting miles (and the expense associated with them) are a personal expense and not deductible on your tax return.

If you have a business, and you are driving for business purposes, you may be able to deduct mileage.

 Here is an article you may find helpful: Can I deduct mileage?