hello and welcome to HCM forum,
i would be glad to answer your query,
according to the dental history provided by you i would like you to know that the gap between your tooth and the gums is due to inflammation of the gum tissue that surrounds the tooth,
this is either a case of localised periodontitis
, where a pocket is formed where all the food gets impacted causing pain and swelling.
Also, as you mentioned that your wisdom teeth have not yet erupted, i would like to inform you that wisdom teeth may or may not erupt, wisdom teeth are not always present.
I advise you to follow a few instructions in order to relief pain and swelling;
1. kindly see a dentist
2. full mouth scaling is required,
3. warm saline rinses(3-4 times/day),
4. use a betadine
i hope i answered your query,
i wish you good health,