How can I get a social security number if I entered the U.S. on a medical visa

A Social Security Number is issued to immigrants who qualify to hold employment (F-1 OPT, H-1, permanent residents, etc.). B visas (for medical treatment) are not allowed to seek gainful employment or labor for hire. The B-1 cannot be converted to H-1 unless you have a sponsoring employer to apply for the new H-1B to immigration. To qualify for an your employer must demonstrate that you have exceptional skills for the position you are being hired for, which must be some type of specialty occupation, and one they are unable to find qualified citizens or legal residents to perform. You will be unable to work nor gain re-entry to the U.S. while the H1 application during the time that your H1 application is being processed. These types of conversions are rarely approved. B visas are not a vehicle to employment or residency.

It will be difficult to seek permission to work on a B visa, as one of the qualifications to obtain such a visa and subsequently granted entry was to prove that you had sufficient funds to support yourself and cover all expenses during your stay. If you say that you need to work, that means you are unable to continue to support yourself -- which is a condition of your entry, ICE will revoke your visa and you will have to leave the country.