In answer to your question a primary syphilis lesion can develop at any site where there is direct contact with an infectious lesion.  Not all contacts result in infection but this is the way syphilis is transmitted- through direct contact.  Once lesions are present, blood tests, rapid or otherwise are positive within a few days of  the appearance of the lesion.   Your negative tests prove that the lesion on your finger was not due to syphilis.  Both your rapid tests and your TP EAI tests prove this.  

Regarding your rash, amoxicillin not uncommonly causes a rash- this may be the culprit for your rash, not syphilis.

I would not be concerned that the lesion on your finger, or the rash were due to syphilis.  EWH

Yes, my first thought was that this rash was some form of reaction to amoxicilline , however it was weird for me that it appeared after the treatment completed and is still ongoing. 

That is why i thought that Syphillis could be the cause for it, although my guess is that it wouldnt cause an itchy and dissapearing/ reappearing rash? I don't know if im right.

 Another thing that was suspicious to me is that i never had a reaction like this to those antibiotics, however I was never put on 2 antibiotics at once.

So, If I got it correctly, the rapid test at 4 months after that wannabe chancre is enough to dismiss Syphillis as the cause?

I will try to work it out with my dermatologist by the end of this week. 

Thank You again. 

You can be 100% confident that you do not have syphilis.  EWH

One more question about the dots on my palms.:

If caused (i know its not) by Syphillis, then the lesions on palms would persist and not go away after few hours? 

Thank You!

Correct.  Syphilis rashes typically do not last for just a few hours- they tend to persist.  If untreated the rash may resolve but the process of resolution takes weeks

Take care.  Please don't worry.  EWH