All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
One of the well-established Shariah principles is that the means to achieve a given end take the same ruling as the end. There is no harm in studying Math and taking "Business App" courses on this subject that incorporates information about simple and compound interest if the purpose is to use it in what is lawful while avoiding the unlawful or helping others to commit it and while disapproving of it. There is also no harm in learning about these unlawful means in order to avoid them and explain them to whoever needs explanation.
However, your statement "I would have to collect a patient's money and ask them how they would be paying for their medical service while at a hospital or any other place" is not clear. If you mean direct handling of the interest-based loans, it is impermissible. There is a difference between studying information about the interest-based loans in order to learn their true nature or the like while intending not to handle them along with disapproving of them and handling them directly. So please clarify what you mean by your statement so that we could answer accordingly.
You mentioned in the question that you are not forced to work as a biller, but you can work as a coding specialist, data analyst, healthcare information technician, release of information specialist, etc. There is no harm in working in these fields if they are free of other Shariah violations such as prohibited (free) mixing between men and women or working in an institution involved in prohibited activities, such as interest-based banks, commercial insurance companies, gambling institutions, and the like. It is impermissible for a Muslim to work in such institutions even if his work is not directly related to interest-based loans.
Allah knows best.