Cough drops contain medications that inhibit the cough reflex. One of these medications is menthol, a commonly used anti-cough medication. Just like any other medication, taking too much is never a good idea. Cough drops are designed to be used for a cough and are not intended to be taken all the time. For these reasons, I suggest refraining from taking cough drops all the time except when you have a cough. Other cough drops contain other drugs such as lidocaine (which can numb the throat). These cough drops should definitely only be used to relieve symptoms.
With that said, it is difficult for most people to overdose on these medications. The amount of menthol in cough drops is usually not enough to cause harm, even if many are taken in a days time. This is why they can be sold over the counter. While the short term effects of taking many in one day are probably small, the effects of taking them daily for many years is probably unknown.
Questions such as these should be directed towards your primary care physician
. I suggest that you schedule an appointment soon. He or she will be able to give you better advise on the potential harms of the cough drops you are taking.