Q.  Should I claim some amount of my Pell grant as taxable income?

A. Yes

Q. How much should I add to my income? 

A. $4000.  The amount of qualified expenses  needed to claim the  maximum AOTC.

Be sure your parents didn't claim the AOTC or Hope Credit 4 timers back when you were their dependent.  The times they used it, on your education counts against your allowable 4 times.

In the TurboTax (TT) interview, you will be asked how much of the scholarship was used for room & board. Answer $4000. That's how you make it taxable, by stating how much was used for non qualified expenses. 

If you spent more than $3151  for books, laptop, and other required course materials, you can reduce the $4000 you need to have taxed.  But, it probably doesn't matter.  Your income is low enough that any amount will most likely reduce your tax to 0.  You should get the $1000 refundable portion as your refund.