I used my own business domain to set up things in the Microsoft admin panel. Initially it suggested something along the lines of ...@businessname.onmicrosoft.com, but I changed it.
Okay that's good Lasse,
You've confirmed its most likely a true Microsoft Small Business account due to both the business domain and Admin panel, since those would be specific to an account running on Microsoft's Azure platform, rather than your personal account that's operating on the Outlook.com platform, regardless of which precise Microsoft domain that particular email account is using.
Based on that, it appears the following Support resources page for Small business would apply, with the most useful section likely the one partway down that page titled, For Admins.
Support resources - Microsoft Support
Note that on the bottom left of that section there's Online and Phone Support including a list of phone numbers by country, which if you're unable to login in order to use the normal Admin console to fix your issue, you'd need to try in order to see whether Microsoft Support can override and do this for you to regain access to your account.
Though I've got no experience with this myself, my assumption is they'll need some sort of proof that you're who you state you are, which if you have any records regarding either the account or other customer information like a customer number if any, or more likely things like when the original invoice or payment occurred, etc., these might help to improve your chances of being able to prove this more quickly.
Once you've regained control of your account, it might be best to set up a second admin account for the business to allow regaining access more easily, or if that costs additional to add, maybe using your personal account as an optional verification method for the business Admin account, if you can't use the phone number twice, once on each system.
I'd also take this opportunity to not only ask Support these specific questions, but also any others that have come to mind, since the bother of going through all of this will be more worth it if you learn better how to both protect and use this account in the future.
Also remember they've heard none of our discussion here, so laying out the basic situation that you have the 3 accounts for Personal, School and the Small Business one you're getting their help with for access via the authenticator could be very helpful to get your issues solved in a single call.
Rob