Are the new appliances that were bought last year able to be claimed on my taxes?

It depends.  If you purchased new appliances for a rental property, you can claim them on your Schedule E.  If you bought new appliances for your home, you can't deduct the cost of your appliances. You may be able to deduct the sales tax you paid if you itemize deductions. Refer to the TurboTax article What Are Itemized Tax Deductions?

Sales tax is deducted on Schedule A when you itemize your deductions.  You have the option of deducting sales tax or State and Local Taxes (SALT).  The most that you can deduct is $10,000 ($5,000 if you are filing as Married Filing Separately). 

For instructions, review the TurboTax Help article Where do I enter my sales taxes paid?

For more information, review the TurboTax article How to Write Off Sales Taxes.

If you need to add your appliances as an expense for your rental property, refer to the TurboTax Help article Where do I enter income and expenses from a rental property?