Early Pregnancy Possibility: Conception Timeline & Beta hCG Results

Question
Age:23
Children: None

I have a very irregular cycle- usually 38 to 42 days.  My last menstrual period started on January 2, 2006.  I had unprotected sex on February 2nd & 3rd.  I know in most cycles that would be too late to conceive, but in my case is it possible to have conceived then?  I had my 1st very faint + hpt on February 13. My 1st beta was 37 on 2/15. Second beta was 107 on 2/17.  Third beta was 1165 on 2/22. I had an ultrasound on 3/8 and saw a heartbeat, but what did they actually see-a sac or a fetus?  They didn't tell me what they saw and I have a picture but it just looks like a little blob.  Also the ultrasoound showed it was 2 mm and gave me an age of 6wks3days, conception date of 2/5/05, and a due date of 10/29/06.

Also- I have had a miscarriage and an ectopic pregnancy.  This pregnancy has given me hope because it is in the uterus and a heartbeat is shown.  But I felt sick for a the past week along with the usual symptoms of tender breasts and fatigue, but this week no sickness.  I think I may have had a little stomach bug but is it normal to lose the morning (all day) sickness? I just want to make sure that everything is going properly and I don't go back to the dr until April 3.  
Thank you very much.

Answer
If the sonogram showed that on March 8 you were 6  weeks 3 days, you probably ovulated on February 6 and could have conceived if you had sex on February 4,5,6,7, or 8. Your due date is October 30. You do not have to have morning sickness. Everything appears to be gong well. Good Luck.