First of all, welcome ... I am an Otolaryngological Surgeon in the New England area, and it's great to have another medical student sign on to CelticsBlog! (What school are you attending? How many years along are you?).
I don't know a great deal about this topic, but most team physicians today are contracted through a medical/healthcare group, (or similar large health organization/university), and do so because of the umbrella of protection provided by large medical groups for malpractice insurance, as the potential for large judgements awarded to high-paid athletes makes it nearly impossible for independent physicians to get into the field.
Hence, your best bet is to contact medical professionals through some of these large healthcare groups or especially colleges/universities, which provide the same kind of umbrella of insurance security. I have a good friend who is one of the team physicians for the University of Miami, and I would be happy to get in touch with him and refer you, as I'm sure he would be willing to help point you in the right direction.
I thought of doing something similar myself early in my career, and most opportunities at that time started with internships at the college level, mainly through university medical centers, or large health organizations associated with colleges and universities. (There were also some doctors who were paying for the opportunity, at least to get started, instead of the other way around). If I'm not mistaken, it's still pretty much the same, as very few independent physicians want to take the chances required in respect to malpractice insurance costs and judgements awarded to high-priced athletes.
Best wishes for your career ... and let me know if I can be of further assistance! Best advice: If this is what you really want to do, don't let anyone discourage you ... it's a very competitive business, and some people love to lessen the competition by sowing doubt and insecurity. God bless!