First ultrasound ?

Hi ladies . I’m curious about something. I will be 6 weeks 5 days at my first appointment . I’m going to insist on an ultrasound for many reasons but will I be able to see a heartbeat that early ?

I also maybe feel like I could have twins .. it’s a very very high possibility in my family. Last night (currently 6 weeks 1 day) when I laid on my bed on my belly I could feel my uterus . Then I laid on my back and above my pubic bone is rock hard .. is it too early for this ?