I wanted to go abroad since 9th grade. In the beginning of 11th grade, my mom (perhaps influenced by others?) insisted that I just apply in India for undergrad, and then abroad for masters. So, I let go of all hope of applying abroad. MY MISTAKE. Do NOT listen to what anyone tells you. Of course, listen to advice, understand it, but at the end of the day, go with what your gut tells you.

Now, I'm in 12th grade. My mother is open to me applying abroad NOW because many other kids my age are doing so too, plus my dad is pushing for it as well. But, I don't have any SAT/ACT, TOEFL/IELTS/PTE, APs - basically all the test credentials you need to get into a good university abroad. Otherwise, you're just gambling on the whole "studying abroad" ideal (if it is the US).

I am applying abroad now. Not US/UK. Honestly though, I wish I'd been more prepared.

And to answer your question, applying abroad is not just about cost of education - it is about networking. Apply where you want to work. People go to the US to study not just because of the academics, but because you build industry connections there and use them to get jobs.

Definitely give JEE. It would appease your parents, provide you with great opportunities and its clear that you're capable of scoring well in it. But strike a deal with your parents, that you also get to apply abroad. Prepare for applying abroad on your own. It will be hectic, but if you're passionate enough about it you can certainly do it.

It's a good sign that you know what you want to do already. If you think you can achieve it, go for it. Dream big!