It depends. Chances are that you only file nonresident returns for each state, to count the income you earned in that state only for the time you were there.
However, if you maintained a residency (such as an apartment, a house, a trailer, etc., but not a hotel room or similar temporary residency), you could be considered a statutory resident of certain states, particularly if you were physically present in the state for more than half of the year. If you had this situation with any particular state, comment that, and we can give you tax information on how that state treats your situation.
Of course, if you can file as nonresident in each state, any income you earn within Texas will not be taxed in the other states.
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