Well, there are two problems:
1) The petitioning employer should be a company that is a health care provider. A general LLC most likely will not work.
2) That you are comfortable with this person will not be persuasive to USCIS. The proper visa will be the H-2B. For an H-2B worker visa, it is expensive and difficult to get because the employer would have to go through an expensive process called a Labor Certification where the position is advertised in the local media, the employer must receive all resumes and eliminate all candidates for valid reasons, not just because they have a job for a specific candidate. This is to prove that this person would not be taking a job away from a U.S. worker. Here is a link:
Also, because they are used up for this year, you will need to apply on April 1, 2016 to start working on October 1, 2016 or later. Here is a link in regards ***** ***** H-2B cap
So unfortunately, USCIS just won't take your word for it. But if you contract a health care provider and have them do a Labor Certification and include evidence of your condition and how rare it is, and if the Labor Certification results in no candidates, then the Labor Certification should be approved.
I wish I had better news for you, but it is important for the U.S. to protect the U.S. job market. At least I believe you have a better chance than most.
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