You may ask for second opinion from an ENT-specialist about the first condition with your throat, to identify if there is really “something weird caught” in your throat ,or not.
Given the symptoms of the second condition (“loose stool”, abdominal pain, and mucus in the stool) you could be experiencing some type of colon inflammation, or colitis. To reveal the nature of possible colitis, you'll need to perform a few medical investigations: standard blood work such as blood count, sedimentation, CRP, liver status; microbiological examination of the stool, and an occult blood test. A colonoscopy can be performed later, if necessary.
It doesn’t seem likely that the symptoms from the throat and colon are connected in any way.
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