Is it normal for a 20 yr. old guy to have a serious relationship w/16yr. old?

It was about a year after my moms passed away when I met her on the road, she had a short black skirt which is like a only a 0.5 inch above her knees and a nice decent top(non-revealing). Of course, as a guy, I complimented her on her appearance(not sexually). We had some laughs and we went our separate ways, only then a day after when I went over to my next-door neighbors/best friends house to hang out for a while and surprisingly finding her there(cousins with my old neighbor). I didn't know that she lived right next door at the time, she was on vacation when I moved back to our old house...she also was a student of my sister, who works at a local High School as a certified Teacher...pretty ironic at the time. A week later, I went to their to my best buddy's house, only to find that she was waiting to see me at a dark corner where no one can see us(nothing happened), we exchanged phone#'s and went on my way. Next thing you know, we started calling each other everynite and day, a week after it went sexual, a week later-on it became engaged(promised...OMG...sex is amazing though...this happened a year ago. We were both Virgins at the time also.