If you mean your last period was May 15th, based on general time frames, you could assume that just about the time you and your fiance were intimate was just about the time in your cycle you would be most likely to for ovulate. On average, most women ovulate about 12-14 days after the first day of their last period. The time which you say you and your fiance were together would for sure fall into that window of time in your cycle. This also explains the very faint positive test by July 4th..up until then, your HGC levels were probably not high enough yet for the test to pick it up...you were probably too soon into the pregnancy at that point.
It's sort of a myth that people's schedules are the same each month. Most people have slight variences in their cycle each month and it all depends on your hormone levels which can fluctuate. This means that if your hormone levels aren't optimum for the egg to release, you could ovulate really late, and in some cases as early as right after your last day of menstruation. The only real way to know when you are ovulating is by monitoring your basal temperature and other body signs, or using an ovulation indicator kit. This explains why alot of women approaching menopause get surprises!
If you're interested in knowing more about tracking your cycle to plan or avoid pregnancy, it can be done very effectively. In fact, using this method (which uses basal temperature and body signs) you can get pretty accurate in determining the peak day/days of ovulation...this method is that precise.
Even if you were an older woman with an unpredicatable cycle approaching menopause. Just go to Amazon.com and type in Natural Family Planning. There are several hospitals in the metro area that offer classes on how to do this. St. Joseph's Hospital in St. Paul has a great program if you're looking for a place to start. At the very least it's a valuable tool for you to better understand your cycle.
As for your pregnancy symptoms..none of my pregnancies were alike as far as symptoms go. One of my pregnancies, I never felt nausea. The others I was sick as a dog. Once again its all about hormones. Don't worry, I'm sure every thing is fine. By the way ..Congrats!