Hello & welcome,
If you can see the root of baby or deciduous tooth coming out of the gingiva
, then that particular tooth is close to shedding or exfoliation.
If gingiva is inflamed, there might be slight infection in it that can be treated with the use of Anti-biotics & painkillers by your dentist
Usually, such naturally exfoliating teeth don't require to be removed by dentist unless creating problems like in the case of your daughter.
If the root is pointing out of the gums then it may be hurting opposing tissue along with the gum. So, best advise here will be not to wait for 4 days . Just approach another dentist & get that tooth extracted as soon as possible before it creates severe discomfort or injures surrounding tissue.
Simply removal of the deciduous tooth will suffice in this condition.