Congratulations and welcome! I recall the first trimester being pretty lousy - even though my symptoms were pretty mild and only slight nausea in lieu of m/s. After the first trimester, the second seems to fly by! Speaking of, I'll be moving up to third trimester here soon (23w1d).
It took DH and I a little while to get used to the idea of twins, since it also doesn't run in either of our families and we had no fertility assistance. We wanted a boy and a girl, but are thrilled to know we so far have two healthy girls growing. U/S's are so exciting! I would freak out right before every visit and then everything would turn out fine and I'd be good for another month before stressing something was wrong. We ended up getting quite a few ultrasounds because every time they couldn't verify both babies' heartbeats, they would confirm with an U/S. The way they check for both heartbeats is by positioning the sonar device over each fetus. You can't really pick up one baby's H/B unless it is directly over it, and the twins are usually positioned in such a way that you can get distinct H/Bs. Also, for our girls, they each have different heartrates - like I said, if they can't hear one or both, they will likely do another U/S.
My weight gain so far is probably about 7-10 pounds. Most of that is recent because I started eating sweets again. Early in the pregnancy, I wanted nothing to do with sweets and I avoided them, ended up losing a few pounds. Last time I was at a doctor's office, they said I was about 5 pounds over what I started at - not bad considering I was 21 weeks along with twins (granted, I'm overweight as it is and don't need to be gaining a lot).
I hope you feel better soon! M/S is no fun!