Deductions & credits

TurboTax will calculate the average outstanding mortgage balance as if you carried it the whole year unless you tell it otherwise. In your situation, I would report Form 1098 on your old home as for your second home, and combine the two 1098s on your new home as a 1098 for your primary home. 

For your old home:

1. In the Federal > Deductions & Credits section of your return, scroll down to Your Home and click Revisit/Start next to Mortgage Interest and Refinancing (Form 1098)
2. Add another 1098 or edit an existing one.
3. Answer the questions and enter or verify the information as it appears on your 1098. Enter this as your Second Home. Make sure you have both the box 1 amount and the property taxes if they are reported on the form. If this loan was ever refinanced, use the original purchase date as your mortgage origination date, in spite of what is on Form 1098.
4. For the Outstanding Mortgage Principal in Box 2, we are going to have to do some math. Take the box 2 amount reported, multiply it by the number of months you had the loan, and divide by 12. If you sold the home in June, multiply by 6 and divide by 12, or just divide the Outstanding Mortgage Principal by 2 and report that as your amount in Box 2. 
5. Answer Tell us about any points paid.
6. Answer Yes to Let's see if this is the most recent form for this loan.
7. Answer Yes to Is this the original loan used to buy your property? unless this is a refinance

For the new home, combine both 1098s together:

1. In the Federal > Deductions & Credits section of your return, scroll down to Your Home and click Revisit/Start next to Mortgage Interest and Refinancing (Form 1098)
2. Add a Form 1098. Enter this as your Primary Home.
3. Answer the questions and enter the information from your Form 1098s:
   1. Box 1 Mortgage interest - Add the amounts together on both 1098s
   2. Box 2 Outstanding Mortgage Principal - Similar to the above loan. If you bought it in May, take the reported amount and multiply by 7, then divide by 12.
   3. Box 3 Mortgage Origination Date - Use the original purchase date from the first Form 1098
   4. Boxes 5 & 6 - Use the combined totals from both 1098s
   5. Make sure Box 7 is checked
4. Answer What kind of property is this loan secured by?
5. Answer We didn't pay any points.
6. Answer Yes to Let's see if this is the most recent form for this loan.
7. Answer Yes to Is this the original loan used to buy your property? 
8. Once you are back in the Home loan deduction summary screen, click Done.
9. Answer NO to Do either of these apply to this loan? for both loans, even if it does apply to the old home.
10. For the outstanding loan balance, use the same amount that you calculated as the outstanding mortgage principal above for both loans. For the old home, enter the sale date. Leave that field blank for your new home.

@tombones