V.B.
Are you breastfeeding? Is your daughter still in your room because you are feeding her in the middle of the night? At 3 months old, it's perfectly safe to put her crib in her own room and have a baby monitor. I don't think you would hear it as much over the monitor as you would right next to your bed. I know it's a farther walk to feed her if she is still getting up for that, but it might be worth it for you to get some sleep. We moved my daughter to her own room at 1 month old (per her doctor's suggestion) and it helped a lot because my husband and my daughter both snored and I NEVER got any sleep. At least I can kick my hubby and make him roll over. ;-)
Best of luck to you. Moving them to their own room is hard, but I think it's the only way you're not going to hear her. I don't think you can stop her from sucking her thumb.