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Lymph node inflammation in the neck, tonsil patches, or nodes does not mean you have mouth cancer. However, because you are experiencing severe oral discomfort while eating and drinking (the pressing feeling you have in the throat ), that is a common symptom of many oral conditions called dysphagia. If your symptoms had aggravated after tooth extraction, then it might be complications of an unhealed extraction site or incorrect local anesthetic injection, both of which are possible.
I would advise you to stop smoking completely or at least reduce the number of cigarettes smoked daily. Smoking increases the risk of developing serious oral conditions that usually start from precancerous lesions. On the other hand, you might have an oral condition due to chronic smoking, which may not be cancerous but certainly painful.
I suggest you consult a maxillofacial surgeon to get your soft palate and tonsil examination done. You can either consult ENT (ear, nose, and throat) specialist or a maxillofacial surgeon. Just antibiotics cannot treat dysphagia; the underlying cause should be known. If a biopsy is needed in the clinic, the surgeon or ENT specialist will send a sample of the tissue or node. On analysis, you will know what kind of cells are there and the correct diagnosis. Your dentist will put you on local medications to ease dysphagia if it is benign (non-cancerous), a normal red or white lesion, or an unhealed extraction site. An unhealed extraction site or even TMJ (temporomandibular joint) problem can give you trismus because there is a recent history of wisdom tooth extraction. So please get the consistency of the lesion or tissue checked at the maxillofacial surgeon's clinic; if needed biopsy will be done. Or else they will prescribe the appropriate medication after manual diagnosis for dysphagia and trismus both.
I hope I was helpful to you.