Remember, guidelines are just guidelines and every pregnancy and every dr is different. I wouldn't worry about gaining 20 pounds in 20 weeks, and I don't think many drs would have a problem either.
And to make you all feel a bit better, with Greg I gained 25 pounds in the first 13 weeks! Yes I was on bedrest, but I also had severe fast food cravings. But for the rest of the pregnancy I'd hear, you've gained more weight now than most women do in their entire pregnancy. Yes, of course I realized it! Way to make me feel better, lol. In the end, I gained about 60 pounds, putting me well over 220, and I am 5'8". By greg's first birthday I had gotten smaller than before I was pregnant.
On the other hand, my friend is 24 weeks pregnant, and she hasn't gained any weight! She is about 5'5", and weighed 113 pounds before pregnancy. She lost weight and got down to 103 pounds in the first trimester, and was so thin her 00's were too loose. She is now 114 pounds and because of her belly has to wear a size 3 (oh no! Lol). And get this... her dr is okay with this and says most women use pregnancy as an excuse to gain weight unneccessarily!
At just over 12 weeks now I've gained 5 pounds. I'm okay with this as it's less than Greg and I am on modified bedrest. I know that I can lose the weight after the baby is born.