I know a bit about medicine.
First, see a doc. In Ottawa, can go to the sexual health clinic on Clarence.
The back rash does not sound like much of anything to worry about. The only one would be syphilis, which clears after. a week or so.
The penile lesions could be herpes. This can DEFINITELY be pass without penetration. HSV is a very infectious virus and all you need is skin to skin contact. No way to know without seeing it, though.