How Do I Lose if I'm Already Skinny?

I'm 4'11 and 100 pounds, but I still find some spots of my body make me look so chunky and I want to improve my health since I've been extremely weak for my entire life..my stomach is slim but my upper arms and thighs are the most affected. I know I should exercise to build muscle, but how do I do that without going overboard and no materials? Is it also okay for me to eat 1100 calories given my height and weight? For me, I get quite full even with just 900 calories in a day, so I'm also worried I won't be able to gain muscle if I don't have the stomach to eat enough. And to get stronger is the biggest factor; I can only lift up something thats 40 pounds before my arms give in, and I cannot do a single pushup. But I can do 80 situps in one sitting!

Edit: thanks everyone! Ill try to work on my habits. Just not sure how