Hi, 
Noted your history and understood the concerns.
Mucus from the nost to throat or swallowing it does not cause mucus in stool.
The cause of mucus in stool is related to the conditions of colon and 
rectum which in turn of its irritation secrete more mucus as a safety.
Hence it is importnat for the following things to be done in your case:
Tests of blood for three consecutive days to see for any medical disease like 
amoebiasis or so to be detected and thus get treated with 
MEtronidazole and an antibiotic if there is any associated intestinal bacterial infection.
Probiotics should be taken in the form of capsules,curds and yogusrt.
If this does not solve your problem then the further tests of 
colonoscopy with 
biopsy will decide the diagnosis and be treatable accordingly.
Cancer should be ruled out as well as any other medical disease which causes irritation of colon.
Hope I have answered your query. Let me know if I can assist you further. 
Regards, 
Dr. T Chandrakant, 
General Surgeon