Hello prerna,
For becoming a fashion designer you need to set your goal straight.
There are a lot of colleges giving you courses regrading fashion designing.
Some of them are-
1.  NID
2.NIFT
3.IIT
4.FDDI
5. AMITY
After 12th you need to opt for B.des or B. F. tech it will cost you around 4-6 lakes for full course and if you want to do masters in it it will cost you 3-4 lakhs.
For more information regarding it