Do I accept an internship offer at a Health Care Real Estate Sale Advisory

Hello,

I am faced with an incredibly difficult dilemma and would really like to hear the opinion of the members of this forum. 

I am a junior international student-athlete at a non-target school at one of the big US cities. I am originally an MIS major, but picked up a major in Finance late in my sophomore year. I have been applying to analyst positions and somehow I landed an internship offer at a Health Care Real Estate company that focuses on sales advisory. I have an opportunity to do a free masters and before I got this offer I intended to do a MS in Applied Mathematics or Data Science as I was told by many people in finance industry to do that instead because it would offer doors to more in-demand jobs.

The dilemma I am facing is that in order to do the MS in Applied Math or DS, I have to drop my Finance degree; and if I drop my finance degree, I can't do this internship because of US work authorization rules for international students. Hypothetically speaking, if I take this internship (and keep my Finance Major) I would do a MS in Business Analytics after the UG.

The firm that offered me the spot is willing to sponsor me now (for CPT). I have not asked them about future sponsorship, but this internship is designed for 2 summers and a full-time position after. I like the people and the lifestyle in that company very very much.

My original dream was to be a strategy consultant- hence for the Finance double major. My dream now (largely because I need 3-year OPT and want larger pay) is to work as a Quant - that's why the MS in Applied Math. But I would still really like to see if I like other fields, so I do not know whether I should accept their offer and give up the MS programs I actually want to do.

Additionally, what will be the exit opportunities if I work in such a niche-market firm? It is obvious I would be giving up the Quant dream, but would Management Consulting still be possible?