How long do I have to wait before I can have a cigarette after wisdom teeth removal?

It sounds like a chemical or allergic reaction to the mouthwash.  First, you should not use it again.  Warm salt water or tea can help the area feel better.  There is a perscription product called Gelclairwhich is almost mraculous in speeding healing and instantly increasing comfort.

I would suggest seeing a board certified oral and maxillofacial surgeon. They are experts at wisdom tooth and broken tooth removal and should be able to offer you options for sedation so the experience will be as pleasant as possible.

The simple answer is no.  The third molar area you have on photograph most likely represents a mixture or healing tissue, blood clot and possible food debris.  Dry socket is ussually with progressive pain that continues to worrsen as several days pass.  Having pain while biting...