“Is it normal to have difficulty breathing after dental anesthesia?”

Sometimes muscle relaxants are used, and if they are not reversed, you may be weak. Also, if you have asthma or COPD, you could have shortness of breath.

No

Without knowing what type of anesthesia you may have had, I will give a more general answer. One factor is your general state of health. Some pre-existing conditions may be worsened. Local anesthesia given in the mouth or jaw might interfere with normal breathing. Nitrous oxide or general anesthesia may also interfere with breathing for a few hours. So, while it could be possible, it is not very common. If symptoms persist or worsen, call your dentist and/or seek medical attention.

This question is very difficult to answer without knowing more details of what you received, the timing and nature of your breathing difficulties, your medical history, etc. you should seek urgent care or Emergency room help if you are having difficulties breathing.

There are multiple reasons for shortness of breath after Dental Surgery.  Pre-existing lung issues, asthma, COPD, smoking, marijauna use  are some.  Others related to anesthesia include mild inhalation of saliva or bleeding from the surgical site, residual action of muscle relaxants (neuromuscular blocking drugs) used during surgery, genetic variations changing drug metabolism.  Is there a family history of problems with anesthesia?  Plasma cholinesterase deficiency is a possibility if succinylcholine was used.
The best source of information is the anesthesiologist who gave you the anesthetic.  Give them a call and arrange a follow-up appointment to review your anesthesia record.

Dental anesthesia is done under local anesthesia. Don't believe difficult breathing is related. Unless you have asthma, copd, or smoking history. You should visit an emergency room.