I don't understand how/why you can't buy a new developer account online? BigOnYa's post is a dead simple, no credit card needed, method. Buy a 20 dollar Visa pre-paid gift card IRL and then just use that online.
Hmm another method I just thought of might be earning 10 dollar MS gift cards through their rewards program (it's free to join). You basically make a bunch of bing searches every day and with luck you could have 20 dollars in a few weeks. Idk if there are any guides about that on GBATemp, but the Reddit community /r/microsoftrewards has a pretty thorough walkthrough on how to get the most points possible every day.
Also bruh, if you already have an account and the school gives you one for free (a hypothetical I know), that's TWO dev accounts. You'll be fine lol.