Sometimes the body will capture stuff, and surround it with mucus. For eg. if it was fungal hyphea, the mucus around it could make it look exactly like a worm. The cells that attack it are very active, and could cause nerve sensations like moving. There is usually an accompanying itch.
But then again, there are worms that do migrate in the mucosal membranes.
If you have a means to magnify the object under light, it would be nice to know if there are internal structures.
worms will have mouth structures, and an anus.
The red could be captured red blood cells, if mucus.
Shroom