FM and Psych are relatively non competitive fields. Your MPH will make you somewhat more competitive, rather than less. Some students do take health related LOA's. You are under no requirement to disclose what the health reason was. Some programs might worry that, whatever the problem was, it could resurface during residency and cause long absences. Mental health issues are a particular concern, as the long hours / sleep interruptions in residency can worsen these. This isn't "fair", and I'm not condoning it, but just telling it like it is.
In any case, the biggest issue is "getting rusty". You've been away from medicine for 2 years. When you return to clinical rotations, you want to do as well as possible. You might be best served by trying to get some clinical experience unofficially before you return, so that you can hit the ground running.
Overall, I think you'll be fine. Most programs will not care that much about the LOA, as long as your clinical performance is good.