I don't know of an app. I take 15% off the top for SE tax (SS/Med) and then a percentage for the bracket I think I'll be in. It starts out rough and gets dialed in as the year goes on. Last year's refund was $33, so as sketchy as it might sound it does work. YMMV.
I pay quarterly. Whether you work a W2 job or not you're gonna owe unless you either increase your withholding to cover SE tax and tax on shopping income, or pay estimated tax.
If you go to irs dot gov and select pay then tax withholding estimator it works kind of like an app and can be used to calculate what you owe. I just recently found it so I can't say how accurate it is. I'll find out next year as I saved the result to compare to.