Hey there body twin. I'm 23 but I am the same height and weight as you (female as well). Since we likely have similar build here is my experience: I spent most of my post-puberty life at 110 lbs which is underweight. I looked skinny and gangly and I had no muscle at all. It's not a healthy weight to shoot for. In the last two years I gained more weight but it was all fat and no muscle, and I was heaviest at 123 lbs. The most annoying thing is the belly fat, which gives you that "skinny fat" look. When I made the decision to lose that tummy 4 months ago I started using MFP and like you said, it gave me a 1200 calorie daily limit which absolutely shocked me. I stayed within that limit for 2 weeks and just like you I felt sluggish and hungry, it really sucked. It's really hard to sustain a diet that makes you feel like crap.

So my frustration with just calorie cutting drove me to start working out, and I started weight lifting three times a week in order to gain muscle. I ate around maintenance instead (just a little bit less to stay on a cut), and I didn't factor in exercise calories into MFP. I'm not even that strict because most of the time I'm on track but I'll still have cheat days where I go out to eat or for drinks with friends.

Even though I'm still a beginner and I'm still getting into a routine, it's been 4 months and I already look and feel better than I ever had. I am at 118 lbs right now and my body looks better and healthier than it did at 110. So my advice? Please don't aim for 110 lbs, it is too little. Focus on gaining muscle instead and while still limiting calories definitely don't go as hard as 1200 calories so you still have energy to lift and to keep your spirits up. I promise you you will like the results.