"Would the income that I received during my time in NYC qualify as NY source income?" Yes.
And more to the point, the income you earned while working from Texas for a New York company is probably also New York Source income.
New York is (almost) unique in that it taxes work done for New York (State) companies, even if you are not physically present in New York.
The big exception is when you work out of state "at the convenience of the employer". That is, if you work from Texas because you live in Texas, you are not in Texas for the convenience of the employer...but if the employer told you, "the job is in Florida" so you move to Florida, then that IS at the convenience of the employer, and so not taxable in NYS.
You can read all about this at this New York State webpage.
So, you file as a New York nonresident, but report all your income as New York source income.
It's not a big burden for many taxpayers, because the tax paid to New York becomes a credit to the resident state taxes...but Texas doesn't have a state tax, so the credit is no good...
You might do an Internet search for "new york telecommuter tax", and you will see plenty of quality articles on this subject.
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