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Sometimes you can apply late to school with a small fine. Check if there is anything else you can do. If NID is the only school you want to get in to you're only option is taking a gap year.
Don't allow yourself to think that its a waste of your time. Instead, try to think of this as an opportunity to prepare for the exam and work on your portfolio and your skills.
Schools like NID look for students who are ambitious and have leadership skills. Students who care deeply about a cause and go out of their way to make a change are some of the things these colleges appreciate.
Take up some internship in the field you're truly interested in. You can commit to it for a whole year. In a field like design, field work is important and make a huge difference on your application. Its also a plus if it pays.
You can also take up a few courses online or look for other college that are still accepting applications.

Hi Neerham!
A specialised Diploma in Public Relations are only offered at post graduation level. You can pursue a Bachelor degree in Mass Communication as it has PR as one of the main subjects. Once you have completed your graduation, you can pursue a PG Diploma in public relations. You can find a list of top colleges in India offering public relations by clicking on this link https://www.shiksha.com/mass-communication-media/articles/top-5-colleges-offering-pr-courses-in-india-blogId-11019
To answer your second question, product manager and a Public Relations are two very different job profiles. A product manager develops products by identifying potential products; conducting market research; generating product requirements; determining specifications, production timetables, pricing, and time-integrated plans for product introduction; developing marketing strategies.
Public relations (PR) is about managing reputation of a company. You'll use all forms of media and communication to build, maintain and manage the reputation of your clients. These range from public bodies or services, to businesses and voluntary organisations. You'll communicate key messages, often using third party endorsements, to defined target audiences in order to establish and maintain goodwill and understanding between an organisation and its public.

Consortium of Medical Engineering and Dental Colleges of Karnataka (COMED K) conducts a state-level examination called COMEDK UGET (Undergraduate Entrance Test) to offer admissions to interested candidates in engineering and medical degree courses offered by colleges/institutes that are affiliated to COMEDK.
COMEDK UGET 2018 exam will be conducted on May 13, 2018, across many cities in India for admissions to various UG programmes. COMEDK UGET scores are accepted by more than 150 engineering colleges, 12 medical colleges and 25 dental colleges in the state of Karnataka.
Please note that there is no entrance test for B.Arch courses as admissions are based on NATA while admissions to MBBS courses are based on NEET.

Physical Fitness criteria :
Candidates, those seek admission to marine courses (DG Shipping-approved courses) have to produce a medical fitness certificate which is approved by the Director General of Shipping. Candidates with Disability (DA), they are not eligible for admission to marine programme. Candidates have to physically fit & meet the medical necessities as specified by DGS guidelines.
Eye Sight criteria
Candidates must have good binocular vision. Their vision should be 6/6 (normal) in each eye separately. Candidates joining B. Tech (Marine Engineering) degree course, their vision should be unaided 0.5 (6/12) in each eye or 0.67 (6/9) in the better eye and 0.33 (6/18) in the other eye. Those applied for DNS, B.Sc. (Nautical Science) & B.Sc. (Maritime Science) degree course, their vision should be unaided 1.0 (6/6) in the better eye and 0.67 (6/9) in the other eye.
* I would advise you to consult a good doctor and take all the necessary measures to ensure that your eye sight improves (if the problem is curable) within months and then, you can apply for the next attempt.