Maybe. You will need to look at your Amazon purchases to see if you paid sales tax. If you paid sales tax on all your Amazon purchases, you don't need to pay use tax on your Ohio tax return.
If you didn't pay sales tax on your Amazon purchases, then according to the Ohio Department of Taxation, you will owe Ohio use tax on those purchases, unless you have a statutory basis for claiming exception or exemption.
According to the Ohio Department of Taxation: "If the seller is not located in Ohio and does not have substantial nexus with Ohio, the seller cannot be required to collect and remit Ohio use tax. However, the purchaser will still owe Ohio use tax on the purchase of goods or services, unless the purchaser has a statutory basis for claiming exception or exemption."
https://www.tax.ohio.gov/sales_and_use/faqs/sales_basics.aspx (see question 12)