Can you video yourself playing ?
If you can't then maybe practice in front of a mirror, and try and recognise where the unwanted sounds are coming from, and identify where your hands are located.
I only play 6 string bass, i use a hybrid of the floating thumb thing. I used to study with Steve Lawson who uses the floating thumb technique. I tried it but didn't get on with it personally. My muting tends to come from both hands, my left hand taking care of the higher strings, and my right hand the lower ones. I move downwards with my plucking hand, so if I'm playing notes on the D string, then my thumb will be resting on E string.
Lessons are a good thing, a good teacher should be able to see what's going on, and offer advice on correcting it.