From the picture you have sent in, it does seem that there is a " hole " in the gum where food can fall in and get stuck inside. What you could do is to get from your dentist an irrigation syringe and blunt needle to flush out food that gets in there.
Alternatively, you could visit your dentist during this period of healing to get him to use his dental equipment to flush out the food.
Do note that this problem will not be permanent as the gums will fully regenerate and the " hole" will no longer be there.
I hope this answer helps and I wish you a speedy recovery!
Kind Regards,
Dr Gerald Tan
