If a mercury thermometer breaks in the mouth or into a beverage, it is possible to ingest mercury. However, elemental mercury is not readily absorbed in the gut, and for the volume contained in a thermometer, is essentially nontoxic by this route.
Mercury vapor is toxic to the nerves (resulting in tingling and tremors) and may be produced when elemental mercury is exposed to heat (like your hot sugar solution). Exposure to mercury vapor can result in nerve damage. For acute exposures of mercury, a blood mercury level is the most accurate test. For chronic mercury exposure, urine mercury levels or finger/toenail mercury levels can be used.
To treat acute mercury intoxication, DMSA chelation is generally the standard of care.
Given your description of the incident, you should be evaluated by your doctor for mercury exposure.