I have a couple of suggestions for you. I am not familiar with any particular parenting technique, but I can tell you what we did with my son which seemed to work.
First of all, if you're going to do this, don't hold her while she naps. She will not be able to learn to sleep on her own at night if she naps in your arms.
Start a bedtime routine and ALWAYS do it. For our son, we take a bath, read a story, sing songs, and then put him down. Once your daughter learns the routine (and she'll learn it quickly), she'll start to feel tired in the middle of your routine, and that helps!
I would continue to swaddle if that helps your daughter to sleep. My son needed to be swaddled to sleep until he was almost 6 months old. As long as your daughter isn't rolling over onto her tummy and unable to roll back over, there is no reason not to swaddle her if it helps.
You might want to try to put your daughter down after you've rocked her to sleep. She may not be ready to learn to sleep on her own. If you are determined, though, always put your daughter down when she is, as we called it, "blinky blinky." Feed her, sing to her, and rock her until she is NEARLY asleep. Don't put her down in the crib wide awake just yet. She isn't too young for that per se, but sounds like she isn't ready for that just yet. If she falls asleep in your arms, wake her slightly (you'll probably do this when you put her in the crib anyway!) It will be sooo much easier for her to fall asleep if she's already most of the way there.
Once you put your daughter to bed, leave your arms around her while she is in the crib and cuddle her. What wakes her is probably the sense of abandonment when you put her down, and then leaving. So put her in the crib and leave your arms around her for a couple of minutes, then ease away. This really helped my son in his first couple of months.
Does she take a paci? I know this is controversial, but you might consider introducing it. My son uses his paci only to sleep, and it has been a godsend.
Instead of going into the room and patting your daughter every 15 minutes, you might actually go in every 5. If that doesn't help, then when you go in every 10-15, pick her up and rock her to help her calm down again. Don't rock her to sleep, but if she is truly screaming and not just fussing, she is not going to put herself to sleep. Calm her down and then put her back down. If this doesn't help after a couple of days, you might give it up, but I would at least try it. I can't listen to my baby scream that long, either.
Finally, and as a last resort, have you considered moving your daughter's bed into your room? To see whether this would help, you might try sleeping in her room once or twice and she if she is more easily calmed when you're in the room, even if you aren't interacting with her. You don't need to be a co-sleeper. You could try instead a bassinet or moving her crib into your room.
Good luck.