Please tell me if it is acceptable for an adult to take teething tablets?

Teething tablets?: I'm not sure what you want to take it for and why you would choose it anyway. It's not a matter of whether or not it's "acceptable". See a dentist or a physician for your issue and find out what would be a better solution.

Too late: There is no purpose for that since you don't have new teeth coming in.

Not recommended: Anbesol or Orajel would probably help you more since they are formulated for adults. See your dentist for diagnosis and treatment. Do not delay.