Can I deduct anything for a newly purchased second home?

Yes, you can deduct points and interest from mortgage on a second home.

You will enter your primary home mortgage information. 

On the Mortgage Deduction Summary screen you will see the Add a lender on the left. 

Regarding adding points on the second home, be aware of the following limitations.

" The buyer may deduct points paid by the seller, provided the buyer subtracts the amount from the basis or cost of the residence. You can only deduct points you pay on loans secured by your second home over the life of the loan. You may be subject to a limit on some of your itemized deductions, including points." 

[From:  https://www.irs.gov/taxtopics/tc504]

The following TurboTax article may be helpful to you with your second home:

https://ttlc.intuit.com/questions/1901495-can-i-deduct-mortgage-points