Crying it out makes me want to cry

So we decided the day after Christmas we would start letting Claire fuss herself to sleep. Up until this point naps and bedtime revolved around mommy rocking her until she was asleep and then laying her in her swing. (She slept in the swing when the acid reflux was at its worst.) We decided it was time for her to sleep in a bed. The AR is under control for the most part and I am exhausted from having to put her to sleep. With Liz we allowed her to fuss for a few minutes and she would eventually fall asleep, usually without too much crying, but I never let Claire cry. I was so spooked from the AR and whenever she cried I picked her up. She is used to falling asleep in mommy's arms and most of the time settles down only for me, so I was staying with her most nights until 9:00 or so and laying her down and then if she woke back up the process began again. Some nights I was not done until 10:30 and I am emotionally, mentally and physically tired. I miss having time with my husband. I miss just sitting on the couch. I miss being able to actually get things done after the kids go to sleep. Liz went to bed at 8:00 at her age and slept all night. I know all babies are different and I am not expecting her to sleep all night (although that would be nice) I just need her to learn to fall asleep on her own. She is almost five months old and I think she is very capable of knowing this by now, but we have never given her a chance. So we started this morning. She went down for her first nap at 10:30. She fussed only a little on and off for 20 minutes and fell asleep. She woke up in 10 minutes and was totally unhappy. I wet up changed her diaper and layed her back down. By this time she was angry. And she was doing that hyperventilating cry. I went up a couple more times and just reassured her mommy is here, I love you. But she was ticked off. She cried for a little while longer and then I got her up because it was close to feeding time and I figured eating would probably do her good. She ate and stayed up for about an hour and half and then I layed her down again. This time she barely cried and fell fast asleep. I know she is exhausted. I am sure this is for her benefit and I know it is for mine, but it is so hard to listen to your baby cry and not pick her up. I know if we dont do this now she will be so much harder to teach this to later, but I still dislike it. As I sit here she has been asleep about 20 minutes and I hear her starting to fuss. Awake again. I know this will be a long process. I am praying it will be quick! I am praying maybe she get the hang of it by 8:00 pm . LOL.