Hello jatin,

No it's not necessary but if you can get better opportunities in different states or country you can definitely go for them, as they will helps you alot to grow.

You can try for best colleges in delhi like IIT Delhi, DTU, Netaji institute of technology, DU etc for your courses, also you can apply for jobs in Noida or gurugram.

But it's important to note that, you can also get opportunities to get admission in different IITs/ NITs or medical colleges from different states and maybe you get a low rank College here, so you have to move to different state for pursuing your education, after that you can try to settle down in delhi.

I hope it helps,

Best of luck.