Taxes Help

Yes.  You will file part-year returns in PA and VA.  In the "My Info" section in TurboTax you will indicate that on Dec 31st you lived in VA and then indicate you lived in another state (PA).  You will use the November date as the date you arrived in VA. This will generate the part-year returns for both states.

PA and VA have a tax reciprocity agreement.  That means your income is taxed only by your state of residence.  During the time you physically lived in PA all income was taxable by PA.  After entering your income and data in the federal "Wages & Income" section you will eventually arrive at the state tax interviews.  In the "Income" section of the PA interview, you will allocate your W2 wages according to the percent of time worked during your PA residency. For example, XX number of pay periods of your W2/total pay periods belong to PA, but you can allocate by any reasonable method (months or days worked in PA/total number of months/days worked for example). Multiply that percentage by the wages earned.  

Once you physically moved to VA in November that became your resident state and your income from that point is taxed by VA; that should be remainder of the wages after the PA portion is allocated.  In the "Income" section of the VA interview you will allocate what belongs to VA.  

Since there was not withholding for PA from May to Nov you will likely owe taxes to PA.