Can a buccal fat pad drop to the jowl?

Buccal fat usually does't "drop" to the jowl area. When a jowl starts to show up or gets worst, it is usually because the normal aging process of the face. 

Great question.  As far as the infection is concerned, a wisdom tooth infection is unlikely to yield troubles to the buccal area secondary to the anatomy surrounding the tooth - that being said, if it had significant inflammation along dentition close to that infected tooth (closer to your molars and even premolars...which would be a pretty nasty infection) then it could potentially affect the buccal fat pad.  Buccal fat infections are NO FUN to deal with.  That being said, with inflammation of the surrounding tissue it can cause laxity of the mandibulo-cutaneous ligament, which can result in some laxity/jowl formation - my internet guess without seeing any pictures or examining you is that some element of this may have happened.  As far as gaining weight, some people do get hypertrophy to the buccal fat area - weight loss can lead to an improvement (particularly if you were able to gain volume in that area with weight gain), however I have had very very very few patients who have ever been happy with the amount of improvement in their contour after weight loss in regards to the buccal area.  Just talking honestly about my patients' personal experience.  Anyway, I hope this helps.  Best of luck.