Thanks for using the forum. I am happy to address your questions, and my answer will be based on the information you provided here. Please make sure you recognize that this forum is for educational purposes only, and it does not substitute for a formal office visit with your doctor.
Without the ability to examine you and obtain a history, I can not tell you what the exact cause of your symptoms is. However I will try to provide you with some useful information.
I can not say for sure if dilantin is the cause of your tremors; there are many causes of tremors. The most common one is enhanced physiologic tremor: everyone has a very slight tremor, and in some people, with stress, excitement, anxiety, caffiene, that remor just comes out. Another common cause of tremor is called essential tremor: this often occurs in multiple family members. Thyroid disorders can also lead to a tremor.
Dilantin can cause tremors and unsteadiness, what is medically termed ataxia. This occurs particularly after long-term use, because of effects on a certain part of the brain called the cerebellum.
Dilantin is a good seizure medications, and in some people highly effect with minimal side effects, but it can potentially have many side effects, and in more recent years, the epilepsy field have started using newer, safer drugs in the long term. Particularly concerning side effects include osteoporosis, and as a side, I recommend you have your bone density checked if you have been on dilantin for >20 years.
You are correct in stating dilantin is used to treat facial pain (such as trigeminal neuralgia), but it would not mask a facial paralysis.
Continued followup with your neurologist, and an evaluation by an epilepsy specialist (a neurologist specialized in seizure medicine) may be of benefit to you as well if there are concerns regarding dilantin, or thoughts about its dose, or need for continuation or switching to another medication.
Thank you for this opportunity to answer your questions, I hope you find the information I have provided useful, good luck.