As a touring performer, do I need to claim that I worked in other states if it shows that I paid State income tax in other states on my W2?

You will need to file a non-resident tax return in each state where you earned money that was more than that state's minimum filing requirement, even if not listed on your W-2.  If you had state withholding for a particular state, you will need to file even if you earned less than the minimum filing requirement, in order to get a refund. 

In some cases, states may have a reciprocity agreement where if you live in one state, you can work in nearby states without filing tax returns in those states. 

Unfortunately, I don't have a list of states with reciprocity agreements, or a list of state minimum filing requirements.  You should start by making a list of all the states where you earned money in-state but were not a resident, and check their filing requirements for non-residents on their web sites.

Or, see a tax professional.  Performers who have been touring longer than you may have recommendations.