I am assuming that you are a single member LLC and have chosen to be a pass-thru entity, that meaning you are not electing to be taxed as a Corporation.
Yes, you did earn money in other states. While the LLC is valuable in that it can protect you personally, you will still pay taxes as an Independent Contractor. You will be subject to Federal and State taxation unless you are under the filing requirement for that state.
NY taxes its residents' income no matter where they earn it. They will, however, give you credit (against your NY tax) for any tax you pay to another state on the same income.
