I got a fast response from Steam Support. They said that the Public option is not availlable because I need to turn on Steam Guard.
It seems You cannot do anything (I also cannot post comments or rate anything) without this annoyng feature activated (I find it really annoyng to have to wait for Confirmation Codes to be sent to my email - and they come very late and sometimes not at all, plus that i don't own a smartphone and I have to login to my email account every time I log onto Steam, not even my Bank Account has so many security features)!
Anyway, I activated Steam Guard and after about 5 attempts I finally got a confirmation code, then I was able to set my mod visibility to Public, after which I disabled Steam Guard again.
The mod is now online and can be found here:
https://steamcommunity.com/sharedfiles/filedetails/?id=2089088310&searchtext=
To anyone else encountering this problem, you must have Steam Guard activated in order to be able to set your mods visibility to Public! At least this is what worked for me.