I just wanted to leave some encouragement! DD is 16 weeks and had reflux (under control with me being dairy free, probiotics, and a homeopathic remedy) and was sleeping on our chests at night and on me for all naps. At 14 weeks we finally decided it needed to stop and did shush-pat for 3 nights - she sleeps on her own at night now. Naps are still very much a work in progress but we are getting there, too.
I know this isn't the case for everyone, but she just seemed ready to sleep on her own - she wasn't sleeping well on me any more. But we also found that shush-pat just didn't work during the day, and so we let her suck the pacifier or a finger until she gets drowsy, then pull it out - she usually wakes up and it takes a number of times before she is tired enough to drift off without it, but shush-pat was just making her scream.
I do wear her for naps here and there, out of necessity when we're out or I go for walks since that's what works best for us right now and we've chosen that over the crib for sometimes. If you're only concerned about the sling because you "should be" and not because you don't want to be doing it that way, then I wouldn't worry about it! It took us a long time to be ready to try to get her down for naps on her own, and even then it was frustrating for a while until we figured out what she needed in order to settle in the crib.