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If she is describing this as a sensation of mucus, it would be very unlikely that there could be a pill caught in the mucus. A pill or solid food would typically fell different and is described as a solid object stuck in the throat.
For thick mucus stuck in the throat, there are several interventions that may help. There are cough medicines that contain guaifenesin, a medicine that helps to thin the mucus to make it easier to clear from the chest or throat. A decongestant also sometimes can help, although decongestants are usually better for congestion in the head that drains into the throat, and there are cough syrups that contain guaifenesin and a decongestant. All of these are available over the counter.
It also can help to breath hot moist air into the throat and chest. This can be done by taking a very hot shower, although breathing hot steam from a pot or bowl is more portable and can be easier to repeat frequently.
There also are some prescription medicines that can be used in someone with severe mucus by relieving inflammation in the throat and chest, most often by inhaled steroids. However, it would be necessary for her to see her doctor to be able to obtain such medicines.
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