Hi,
There's pros and cons to your situation.
The con is obvious, your freshman GPA — however, if it's just your freshman GPA then that's better than the reverse — having a +3.0 GPA, then having a 1.5 your senior year would have been a death blow. The most positive thing about your situation is that it's getting better, or at least it seems that way.
When you transfer to the other institution, I'm assuming you'll be a junior in units (like most transfer students). Also, given depending on how many units you've taken it may be pretty difficult to move your GPA much higher by graduation. So, you may want to sit down and calculate how many courses/units you'd need to bump your GPA more before graduation. As, the person above me stated, you'll need to start working on some extracurriculars other than shadowing. Shadowing is rewarding, but it is a passive position. So, try to get involved in research or start a project on something you care about — if there's time do research and display long term leadership in something meaningful, this my require a post grad gap year if you have something worthwhile in the pipeline (for example I delayed my graduation as I used a research project to tour around conferences as a premed).
However, above all else you should be realistic. I'm not well versed on all of the recent requirements and statistics, you should visit the AAMC page first and see how you fit in as an applicant, then follow that up with more research with schools that you might fit into. Also, you should open up your options. The obvious other option are DO programs, because of the larger range in applicant pools you'd be more competitive there. But, please don't limit yourself to just those two health care providers. Not to dissuade you, but you want to have the conversation with yourself now before you're in medical school about why not a Nurse Practitioner or Physician Assistant? Just food for thought, especially if you're trending towards primary care and time flexibility (family). You may have very strong reason to become a physician, if so let the latter part of the paragraph fall on deaf ears.
Getting into medical school is pretty cool, but not getting in or not being able to should not be seen as a failure. It sounds like you had a rough personal life patch, as do a lot of applicants. You still have a shot, but it will come with a lot of work (ECs, MCAT, PS, LORs, primaries/secondary, interview), and of course taking responsibility for both your highs and lows on your CV. Overall, if you do well on the MCAT and if you've faced a legacy of discrimination (under-represented) you have an okay shot if you keep going this direction.
But, be sure to keep your options open.