Dark patches under your arms can be pretty normal- but no one can tell you for sure what it is here- you need to get to a doctor to have an in person exam done (photos will not help give you an accurate diagnosis which is why you can't post them on the forum). Your doctor will also need more of your medical history- as far as if you got syphilis, we can't state your chances of that, being that we don't know anything about your sexual history or reasons you are concerned about that- so it's best to get to a doctor. In addition, syphilis wouldn't really be dark patches- it starts as a sore in one location (usually in mouth, rectal, or genital area) and then turns into a rash over your body as part of the second stage.