Do I have to have a business license to claim it on my taxes?

For the sake of taxes, you don’t have to have a business license but you do need some sort of claim to business.
The first order of business, should be a separate bank account, strictly for your business. It doesn’t have to be a business account, you can also have a personal account for your business, by listing your name along with ‘dba Your business name’.
Keeping careful books for the business, is important. If the IRS ever comes to visit, they will be looking for the ‘business books’.
You don’t have to be formal, to be considered a business.