HUGS! I know it stinks to hear your baby cry or be upset. I don't think there is any magic book for these phases and you are probably right it is a phase. Remember motrin takes a good 30 minutes to kick in and if she is all worked up with pain then that may be why it takes so long to get her settled back in. Try giving her the motrin 30 minutes at least before you plan to lay her down.
Since you have realized she is teething, have her checked for reflux as well, which can burn when laying down. A lot of children have this. A easy prescription can remedy it until she outgrows it. My daughter had it young, early on, thought it was colic and turned out to be reflux. She outgrew it within months.
I wouldn't pick her up but do go in and rub her back, try and settle her back in and there is nothing wrong with letting her know you are there. Try a voice activated music box. That is still a huge hit in my house. It goes off with any noise and winds down in five minutes playing a sweet lullaby.
With both of my kids I would rub their backs, turn off the lights and sit there with the music box on and get them to lay down and would walk away.
If they woke or fussed or cried the music box starts back up. It has a switch on it for ocean waves too or even a nightlight mode that kicks on. Sometimes it worked sometimes it didn't. White noise has always helped my kids get calm and sleep better though.
She needs naps/good sleep at night for health as well as growth. I would lay her down and not go back until 15 minutes, then rub her back, whisper it is time for rest and walk away. You may have to continue this. It could be seperation anxiety, which is typically short lived but it could be reflux as well.
Rocking her or falling asleep on you is great, for now but will lead to unhealthy habits that you will have a LONG time to break. Go to her if you can without picking her up. Whisper, sing and rub her back and try to settle her down.
I didn't ever have to do crying it out for long with either of my children thankfully, but I did at least wait 15 minutes before I went to them. Even a fan in her room for white noise can help. Black out shades to keep her room dark at naptimes can help.