It should read "Wir sind jetzt drei Monate zusammen und ich bin immer noch glücklich mit dir."
Gamine, there is no "n" after "Monate" - only if you say "Wir sind seit drei Monaten zusammen...".
About the tense - it's perfectly fine the way it is now, I think the possible English translation shouldn't bother us at that stage, because the original request is in German and not in English. (anyway: in English you would have to use Present Perfect Tense)
And yeah, Francky or Bamsa or any other expert: it would be way easier if you waited for our opinion first, before editing. (yet - no offense!) I usually try to respond to this kind of requests quite fast.
Hello Heidrun. Thanks for your message thanks for having explained the use of the tense to me. Helps me a lot. Now I know it for the next time. And, no problem, will wait for your opinion next time.