No Internship this Summer, unsure of how to proceed

Hi everyone, I'm a current junior at a target school, 3.5 gpa. I had an internship offer at an asset management firm until 2 days ago when they rescinded the offer because I may need sponsorship in like 4 years due to being an international student, and they are strict on not sponsoring candidates under any circumstances. My school office of international affairs told me that this would not be an issue but when I sent them my CPT letter (a thing that intl students need to do) they rescinded my offer. Feeling absolutely hopeless seeing that it's mid march and unsure of what to do as at present i have nothing lined up for the summer. I don't particularly want to work in IB, but I'd like to be front office ideally. Working in investments or trading are both preferences, but obviously at this point I'd take anything I can get. I mostly have a couple of questions: 

1. How fucked am i if I 1. don't get a finance internship this summer but instead do something in tech/data science/maybe a role as a products intern or something or 2. if i get a finance related internship (maybe big 4 consulting/back office) but in my home country

2. is it better to work at a boutique no-name firm in the US or a bigger firm in my home country if my end goal is full-time in the US. 

3. what steps should i take besides cold emailing banks/pe shops/prop shops and reaching out to alumni? i'm doing that quite a bit (at least 20 emails/day) but feel like my efforts are fruitless