How to show proof of publication?
You don't get a "certificate" for publishing something. The fact that it is available online at the journal's website (which can take a while, depending on their publishing speeds) and has a doi (which you should receive soon after acceptance), is sufficient proof. 
Most societies don't have a membership card either. They might send you a welcome letter, which you could use as proof of membership.


Most places accept different forms of proof of claim when a formal one doesn't exist. In your cases, the following should be just as valid:


An email from the editor, accepting your paper for publication (you should have this)
An email from the society, thanking you for your interest and membership
A screenshot of your member page, showing validity
A screenshot of the web copy of your paper (some journals throw a rough version on the web which serves till the final version is typeset).