. thanks for sharing your concern
that flap is part of gingiva
,donot worry.on healing it will be fine.if its posing greater discomfort to you, then you can visit your dentist
and either get it sutured or excised,based upon how big or small it is.
i would suggest you for a post extraction follow up to check for any interference in healing process,could be maintainence of hygiene problem.
as the location of third molars or its extracted socket makes it difficult to clean.
regarding your antibiotic,i donot think it is required but your physician needs to be consulted before taking any medication, as you are on hydrea
also remember healing in your case is little slow in comparison to others,so donot worry .
you will be fine.
.till then maintain good oral hygiene
.and you can occasionally take painkillers if required.