Thank you, Richard! I was able to switch my country back to the states from the subscription page, and from there I was able to add payment information. From an outsiders perspective, I felt like I was in a loop because my profile information would not let me change my country without a payment, and I couldn't make a payment because my credit card is from my home country. It was not until you pointed out the change country option on the subscription (not profile) page that I realized I could do it that way. I'd be surprised if I was the first confused by that.
I'm a music student, so Spotify is too good of a resource to pass up, so thanks for helping me access it abroad!