Couple of problems here. Sculpting is working, but parts of your mesh are not ! 🙂 The first is the normal direction of the polys in the waistcoat, which are wrong (blue), and therefore you won't be able to sculpt on the front sides of these meshes until those are fixed by selecting the wrong polys (I think it's all of them, so Ctrl-A) and finding Reverse Normals from the r-click menu. The shirt has a similar problem caused by it having no actual thickness, which means we see in the inverted normals in the folded collar area as well.
Secondly, because all these meshes are a single object, sculpting them on an individual basis will be extremely difficult and it will be almost impossible to avoid one section intersecting another. I would seriously suggest splitting the model into its various parts to allow you to sculpt each mesh alone, which will get you much more control over the individual parts and should prevent you moving other bits unintentionally.
I also notice you have activated sculpting but only at Level 0, with no subdivision, which is unusual.
Lastly, you are making life very difficult for yourself by having mesh inside mesh inside mesh. The rather superior approach is to not have any body mesh under clothes unless those clothes will be removed during any subsequent animation. So, there is no need for actual poly arms, chest or torso if it is hidden by clothing. Likewise there is no need to model the whole shirt when the vast majority of it is covered by waistcoat ! So really, the body mesh here should consist of the head, down to just under the neckline, and the hands - the rest of it is covered by clothing or shoes, and all the time it is there is just an additional intersection risk for you with every modelling or sculpting tool you deploy on it, and when it moves later when rigged, if that is what you will be doing with it.
CBR