I'm fairly new to sculpting in Blender, and I'm attempting to sculpt characters for my animated short. The characters are going to be talking and moving their mouths, so I'm trying to sculpt the inside of the mouth. I started by adding a big hole where the mouth should go and then I sculpting the lips and used the grab and masking tools to try and close the mouth, but all that did was flatten the inside. Any tips on how to accomplish this would be appreciated.
Don't sculpt the inside of the mouth if you want to animate the character's face.
A sculpted mesh is bad for animation because it is very dense. This means your computer has to do a lot of unnecessary calculations => Blender will freeze very often or even crash. The UV map is huge and a mess, texturing will be a pain and weight painting a hell. In the end, the mesh can still deform very badly.
If you want to animate your character's face, do a retopology of the mesh.
Once you have a clean topology you can model the inside of the mouth easily just by extruding the edge loop of the lips.
To smooth the nose try Shade Smooth mode. If this doesn't help, try the Smooth brush with low strength (0.15 to 0.20).
If you still need to create the inside of a mouth then have a look here: What sculpting tools would I use to separate a jaw from the skull?
Bonus tip: You can paint Face Sets with the Edit Face Set brush, then hover the mouse over the face set, and hide it with H - or Shift+H to hide everything else. (Alt+H to reveal the hidden.). This way you can create a mask from a face set. (Hide everything else, create a mask from visible.)