First of all, you don’t need a business bank account, or any seller permits to sell print-on-demand online. You just need to report your personal income tax under the category of Other Income.
There are so many different ways to file your taxes whether you're using TurboTax, you're using an automated system, or you have a tax person, or if you fill out the forms yourself.
So specifically for teespring.com, you only pay taxes on the profits that you actually paid out from your Teespring account in that year. For Merch by Amazon and Redbubble, they pay out automatically, so whatever you receive in that year that you're paying taxes on, that's what you will put in the Other Income.