I would refer you to https://blog.taxjar.com/drop-shipping-scenarios-sales-tax/ at Taxjar's website to get clarification on whether you need to collect sales taxes or not. Ned Lenhart does a real nice job demystifying this complex issue.
Open Sky Consulting, LLC
Many States are making it easier to collect sales tax by expanding the definition of nexus in their State, we have seen some States say that a simple dropship location creates nexus, others are approaching this by the number of transactions, others by the location of a wharehouse. In our Accounting Firm we suggest most of our clients look at TaxJar as a solution to streamline their Sales Tax Reporting process.
I would also suggest working with an Accounting Firm that is intemetly involved with eCommerce businesses, when dealing with Sales Tax you do want to make sure you have a good Accounting process in place. A good Accounting Firm can help make sure you are capturing all require information.