State tax filing

You wouldn't owe taxes to Maryland if you did all the work in Texas. Per this excerpt from the instructions to Maryland Form 505, your income would only be taxed in Maryland if it was from a business, trade, profession or occupation carried on in Maryland. Even though your employer is located in Maryland, unless you physically worked there or were an owner in your employer's business, you would not be considered to being carrying on business activities in that state. So, you just need to file as a part-year resident in Maryland for the months you worked or lived there.