In box 16, W2 shows state wages for only one state but I lived in two states. Will I need a corrected W2 or can I reallocate wages to each state

Yes, you can allocate the appropriate wages to each residency period. A corrected W2 is not needed. 

You can go directly to the W2 to make the entries using these steps.

1. Select My Account in the upper right
2. Select Tools
3. Select Topic Search (see image attached)
4. Search for W2 and select GO
5. Add another row to report two states on one W2

You cannot reallocate any state withholding because we have to assume the employer paid your state income tax withholding to the state listed on the W2.

File each state return as a part-year resident