For the last 6 weeks of 2018, I lived in NY but worked in VA. Employer withheld for both states. Am I entitled to a non-resident refund from VA for the taxes withheld?

Not exactly.  VA can tax you as a non-resident on earnings from work actually performed in VA.  But NY will give you a credit on its return for the taxes you paid to VA.  To get the credit, you must file a non-resident VA return in addition to your home state NY return.  In TurboTax, you must complete the non-resident return first, before you do your home state return, in order for the credit to flow properly.

https://ttlc.intuit.com/questions/1901271-how-do-i-file-a-nonresident-state-return