Giving third parties data like that is some terrible idea.  

I don't think it is a god idea to put one's my medical info on some 3rd party website.

Agreed, not only for this, but for any type of medical information.  It is not clear from this app's website, at least on a quick pass, that this company is subject to HIPPAA or state laws concerning confidentiality of medical information.  And even if the information itself is confidential, it's not clear that the FACT somone has had STD testing won't be shared with all kinds of vendors.  I can imagine signing up for this and getting bombarded with spam for condoms, lube, drug tests, hair replacement therapy, you name it.  And once you share it, what's to stop the receiver from forwarding it or publishing it?