Where I am, in New York City, it is pretty common to work with med students, residents, and attendings who are Sikh and have not cut their hair. One of my closest friends is a Sikh surgery resident with uncut hair. As far as getting residency, I don't think he experienced any more discrimination than any other foreign medical grad (as you probably know, FMGs are often stuck with the residency spots that no one else wants). It helps that he is an AIIMS graduate. But in terms of the general public, yes, there is discrimination. He lives in the Bronx, and he has gotten rude comments from people around where he lives. This was especially bad after 9/11, as people seemed to assume that he was Muslim. One woman shouted at him and told him to "go back to Saudi Arabia," which is ridiculous since he clearly looks like a Punjabi Sikh. He has never faced any violence, but the rude comments really bother him. In Manhattan, he doesn't have to deal with that, for the most part.
The discrimination would almost certainly be worse in suburban and rural areas.
On the other hand, there are communities in the city that are almost entirely Punjabi, especially out in Queens, where you would fit in very easily.
If you are thinking about coming to New York, send me a private message. I have a lot of Punjabi friends.
