There's some interesting perspectives in the answers you have received so far. Here's my two cents, for what its worth....
I guess you have to weigh how much you have invested against the risk and expense of either not finishing or not matching. It's a very personal decision, and there are very real risks in your situation. Matching as an IMG is tough enough without red flags. As DrStephenStrange says, its possible your residency application might be filtered out before you can tell your story. That's worth considering.
Still, I dont think there is a clear cut right or wrong. It's your choice, and you who has to live with the consequences, good or bad, of whatever decision you make.
How will you feel if you invest further in your education and don't match? How will you feel if you give up on your dream; will you always wonder if it could have worked out? Will you be bitter? Can you afford to invest more in pursuing this dream? Can you afford to loose this investment if you're not successful? What support do you have for continuing? What are your options if you don’t continue? You need to weigh these factors.
A withdrawal will look better than a dismissal if you decide to continue along this path. It will likely be obvious from your transcript that you have been struggling. You will need to make a case for why you struggled (health problems), and why they should believe you will be more successful at their school.
Same for residency applications, your application will need to address the challenges you faced, how you overcame them, and how all that will make you a better doctor.
Correct me if I'm wrong, but I'm guessing from your description of what has happened that you have already gone through SGU's Review Dismissal and Appeals process as outlined in their handbook and lost your appeal. If not, you should be appealing.
The SGU handbook states, "If a student’s appeal is unsuccessful, the letter to the student with a rejected appeal will provide the student with the option to withdraw from the MD program within a specified timeframe. If the student does not withdraw within the specified timeframe, the student will be dismissed." This sounds like what is happening with you.
Its possible those assessing your applications will read between the lines and wonder why SGU wasn't more accommodating.
RUSM's transfer policy is here:
TRANSFER TO ROSS UNIVERSITY SCHOOL OF MEDICINE. I see some potential challenges for you in their requirements, but look for yourself.
Others may have personal experience, but I have heard that many of the "big three" are reluctant to accept transfers.
You loose nothing by applying, however, except the application fee, and you have a lot invested in your education right now. Application fees are pretty minimal compared to what you have invested so far. I dont think RUSM even charges an application fee right now.
If you are determined to continue, I would agree with Emmet2301, apply broadly, including to AUC and other Caribbean schools. You only loose the cost of the application fee, which is minimal next to what you have already invested (and will invest to finish).
If you decide you want to continue, don't let anyone on this forum tell you it's not possible to transfer. Apply and see if you can get into a new school.
TopNepNep says there are plenty of transfers to Saint James at fifth semester. Here's the webpage for SJSM transfers:
Transfer to St. James School of Medicine - Transferring Medical School
AUC's requirements for transfer are here:
Transfer To AUC School of Medicine. They do note, "individual course credits are not guaranteed to transfer." I'm guessing this will be the case for most schools and you may be required to repeat some curriculum.
Any school that cares about their Step 1 pass rate will want to make sure you are capable of passing Step before they let you write it, so expect to jump through some hoops to convince them. If the school isn't concerned about this, that should be a red flag, they probably just want yiur money and dont care about helping you succeed (some would argue all Caribbean schools are like this). I'm guessing you should expect to loose a semester in the transfer process.
This thread makes some observations about transfering that you may find relevant:
transferring to sgu.
Good luck with whatever path you choose..