Is it worth a trip to the doctor for dental problem?

Terminology. If you mean a trip to a dds or a dmd for resolution of dental problems, absolutely. If you mean a trip to a md or a do for resolution of dental problems, wrong doctor. Take advantage of a dentist's many years of training and experience to treat your dental problems, you'll be glad you did. Don't wait, call now.
Yes. A trip to the dentist will get you on the road to good health. Be evaluated to prevent and treat gum disease, tooth decay, replace missing teeth, screen for oral cancer plus many other things. It is also good to have a ongoing relationship with your dentist in case a unexpected emergency occurs.
Absolutely. If you are in pain, it indicates that a problem which may have started out as something small has become acute. The best dental attitude is to see your dentist before you experience pain. Prevention is the key!