Can I do fashion designing? I have color vision problem?

also tell me the best institute or university to get degree in fashion designing in chandigarh ?

If you have color blindness, in my view it would be difficult to work in an area that involves matching colors.

Online color blindness test:
http://colorvisiontesting.com/online%20test.htm

Google "fashion designing in chandigarh" for a list of fashion design schools in your area.

Actually, I know some excellent graphic designers who are mildly to severely color blind. They all do AMAZING work with black and white. They all have highly sophisticated understandings of shape, line, form, white space, contrast, etc. I say go for it! Emphasize your strengths.