This makes me so sad. You're doing amazing sweetie.
'Overqualified' WTF is wrong with people? You'll find out there are so many weirdos out there, especially South Asian guys who are just mummy boys and looking for someone to be their mother instead of wife. So try not to base your self-worth on these 'rejections' (sounds like you dodged some bullets). Please try not to feel pressured by any family members. You are good. If you really want to get married it doesn't hurt to look around now, but focus on finishing your degree, then after FY1 or FY2 (preferably) would be a good time to get married as you have finished your training and have some savings too.
Please do not sell yourself short to impress a guy. The guy for you should be proud of your accomplishments, the fact you're a Doctor (soon) and push you to do more things, not looking for someone to just cook and clean. What losers!
Also, actually a lot of guys in our generation don't care THAT much about skin colour, it's mostly their parents (who were born in South Asia etc) who have an issue with it. In my opinion, I'd suggest looking for guys who are educated and have professional jobs, they tend to be the ones who are much more down to earth and reasonable. It would complement alongside your 'qualifications' lol. Also please try and vet the groom and family you are marrying into beforehand if you can (asking around, Facebook etc etc). As a South Asian guy myself, I've seen this seems to be quite important. South Asian families like to hide a lot of s*it (e.g. scandals, cons, general reputation of the family, divorces etc... I know one family failed to mention they have a family history of mental illnesses to the groom, the brides brother is has schizophrenia).