Root has been left in and sinus perforated?

I suggest immediately seeing an oral surgeon in order to evaluate for sinus exposure. The oral surgeon should be able to easily correct if sinus exposure is an issue.

Furthermore, the root should be removed to avoid any problems that may arise down the road.

It sounds to me that your dentist might have perforated the sinus.  This is a common occurrence when extracting upper molars.  The dentist will try to achieve primary closure, give you some antibiotics, pain medication, and sudafed.  In addition, it seemed that your root might have been lodged into your sinus.  This is a more serious issue.  I would suggest that you go to an oral surgeon and get a Xray or CBCT to see if the root is in your sinus.  It is usually preferable to NOT leave any root behind to minimize the probability of future infection.