Why am I experiencing pain after getting my crown put on?

There are many possibilities :If your Crown is sensitive to hot fluids, there could be a nerve problem, If to cold it might be reversible.If the dental crown is sensitive to chewing pressure, then the crown might be high, to your bite or occlusion.Did your dentist warned you about any sensitivity before cementing your crown ? MAYBE DUE TO DEEP CARIES ? and possibility of root canal exists ?The above are just possibilities, but there are many other factors that can cause sensitivity and discomfort, including nerves, gums, bite, and the method of cements used to seat your dental crown, and the type of crown you have. Is your crown an Emax? zirconia ? of porcelain fused to metal ? each crown have specific cement protocol, and if not followed can cause sensitivity, or pain also.

There are many reasons why you may have pain but the most common is a high spot.  If every time you close that tooth hits first you can be "bruised" even if the high spot is small .  Hot and cold sensitivity are bruising of the pulp (reversible pulpits) but can be a sign of a dying pulp (nerve and may be an irreversible pulpitis which can require a root canal.   Not being sensitive to hot and cold is usually a good sign that there is no pulpits or it may be that the pulp tissue is already necrotic (dead) which is a reason to need a root canal treatment.Tenderness to bite is an apical periodontitis, and is most likely just a "bruising " from excessive forces on the tooth.  It is possible that there is a necrotic pulp that is leaking septic materials into your b one and you are developing an abscess.It is probably not a case of the dentist drilling too deep or you would have an acute pulpitis with sensitivity to hot and cold.Remember when a dentist recommends a crown on one tooth it is usually the worst tooth in your whole mouth, it is rare for a dentist to accidentally drill too deep but if the decay is deep the dentist must take out all the decay.

Usually sensitivity or pain to chewing
is caused by the crown hitting first or improperly when you bite down.
This can often times be easily adjusted by your dentist to avoid the
pain. There is always a chance that when dental restorations are placed
that it could progress to needing a root canal due to the amount of decay, but
have them check the bite first and if need be, have the crown adjusted.

It sounds like you may have a high spot somewhere. I would make an appointment with your dentist to have him reevaluate it. If there is a high spot, it may take some time after the adjustment before you get relief. Worse case scenario is a root canal