Hi there, I'm so sorry that your post was sitting for so long, without a response.
Okay, self soothing is a learned skill, that literally takes weeks. It's not something that will happen overnight, or within a few days. Your little one is just 3 months old, so she's just starting the process.
It is lot harder to go without the soother, I've had one soother-baby and a non-soother baby-- life was a lot smoother with a soother-baby. With my non-soother baby (Brendan) he had a hard time settling down and completely entering sleep with the soother. It would disrupt the process and he would never really fall asleep. So we ended up going without the soother.
I will be honest with you, we had lots of tears. I found that as he matured, from 3 months to 4.5 months, his ability to settle into sleep gradually improved. It took lots of patience and keeping calm on my part. Lots of patting-shushing, and staying near to support through the jolts.
Right now, you're just a week into it-- a week from now, it'll be better-- not completely better but you should notice somewhat of a difference. During this time, be as conscious of her sleepy cues and making sure she doesn't overtire/overstimulate prior to her nap. You don't want to push her awake time right now, just focus on helping her to settle to sleep without the prop.
I hope this helps, I know it's not easy right now, but it will improve as she matures each week.