3 Weeks Pregnant And Cramping?

My last period was April 7th it started off normal but towards the end of my period I had very heavy bleeding for a few hours. I was due to start my period again May 4th and it did not start but I have had cramping. I went to the hospital on Friday and they did a ultrasound and said they did not see anything they also used the l probe and did not see anything. I took a pregnancy test on the 4th and it was positive. I just wanted to know if all of this is normal. The only time I had was April 15th and April 16th so I would only be around 3 weeks after conception. Is it normal not to see anything at all using a regular ultrasound and l probe? Is it possible I was pregnant back in April when I had my period and lost it but it is still showing up positive? The cramping I have been having is in my lower abdomen and it started about a week in a half ago but as of today it seems to be on the left side of my lower abdomen.