So I’ll be very frank with you.
If your budget is a maximum of $10000 per year, there are very few offers like that available for Internationals across the whole US college system. Many colleges will not make any such offers. Among the subset of US colleges that will make some such offers, there are very few available. Most of those colleges are what is called need aware for Internationals, and so they will only make such offers to the few high need International applicants they want the most. A very few are what is called need blind for Internationals, but this is not much help because those few colleges have incredibly low admissions rates for Internationals in general.
So either way, there are not many such offers truly available, and it is incredibly competitive to get one.
OK, given this, the fundamental question is whether you will be competitive for any of those offers. And again the frank answer is that I don’t know.
In part that is because we don’t know your SAT score yet, and at this level of competition there is a big difference between a 1450 and a 1550.
Additionally, we don’t know what a 3.7 unweighted GPA means in the context of your school and course rigor. I can tell you that in a more or less normal college prep US high school with a normal amount of grade inflation, assuming decently high course rigor, that would be a good GPA for US college admissions generally, but it probably would not be competitive enough in your context.
But perhaps a 3.7 means more in your system than it would in such a US high school. To figure this out, ideally you need prior US admissions data from your school, or at least similar schools. If nothing else, though, it would be helpful to know where (or approximately where) that ranks you in your secondary school class, compared to how many people in your secondary school go to US colleges.
Finally, applying for CS/engineering would not necessarily be a problem if you were able to pay, as there are many very good colleges for that in the US that are happy to take some Internationals who can pay. But most of those then fall into the category of having no aid for Internationals.
And then among the remainder, CS is more common, but engineering is far less common. Meaning if you need engineering to be an option, the number of offers like that available across the whole US is an even smaller number than before.
And then CS is just an incredibly popular major these days, not least among Internationals. So if you are thinking in terms of how to stand out among all the other International applicants a US college with International aid is likely getting these days, such that it is willing to give you one of its few available big aid offers over all those other Internationals who would want that offer–again, to be very frank I think it could well hurt to be a CS intender. Not impossible, but it might mean things like your SAT and grades would have to be even more competitive than usual, possibly ECs as well, and so on.
So I don’t love giving you this message, but at this point I truly do not know if there will be any offers at that level available for you in the US. But if you can provide us some clarity on how competitive your GPA is, an actual SAT score, and whether you need engineering to be an option or just CS, we might be able to recommend at least what might be among your better chances. But they still might all be low.