You sound engaged to me
In general I'd say it's a "real" engagement period when a wedding date (or season/month) is within a year or so.
I didn't have an engagement ring, it just wasn't important to us and frankly I didn't realize until our engagement period that so many people did (not a thing in my family).
Anyway, I learned to lead with "B and I are getting married in June..." to head off questions about whether or not we were really engaged.
The only person who persisted was my now-husband's grandmother, who kept asking "What to call this" in reference to the lack of ring. "Is it engaged to be engaged??" etc etc. I finally just told her that they can call it whatever they want, but the wedding's on ___ date. I really recommend that method; it satisfied her.
I was engaged my senior year of college and almost embarrassed to use the word fiance, just because so many college girls proclaim themselves engaged regularly without ever getting married. It gets silly.