NIFT

Yes, you can definitely make a career in fashion after doing engineering. Who says you can't? If you think again for a second, you will realize how hand in hand fashion and engineering go. What is fashion, if not newer innovation of trends and technology related to it. If you feel passionate about designing and fashion, you should definitely go for it. Now comes the part about how to go about it. Here it is:
If you want to go for design, there are a whole lot of options that you can explore. You can look into Fashion Design, Apparel Design, Jewelry Design, Interior Design, Fashion Communication, Fashion Technology, Fashion Management, etc. Check this link for more information on these courses: Make Career in Design, Design guide, Design Institute in Delhi
There are courses available in NIFT and other reputed institutes in the above domains. Try and research more about it. Some will provide you with a Bachelor's degree, but at this time I would suggest you to do a Masters in fashion management/Diploma in Fashion management/Fashion Communication. Since you have an engineering background, I would suggest you to look at design courses in NID, their curriculum and eligibility. If you can manage to crack their Masters level entrances, it would prove to be a huge boost for your career in fashion. Lastly, I hope you have thought about your choice regarding choosing the field of fashion, because after this level (postgraduate), it would be very difficult for you to change your field again.