Hi..
Welcome to HEALTHCARE MAGIC..
I have gone through your query and can understand your concerns..
As per your complain it seems that you have infection in  the gums leading to inflammation and it can cause pain that can also be elicited in the teeth..
Secondly sensitivity of the teeth can also be due to Dentinal 
Hypersensitivity that occurs due to gum recession as well as opening up of the nerve endings present over the surface of the teeth and it leads to sensitive teeth..
Consult an Oral Physician and get evaluated and a thorough clinical evaluation and investigations like x ray can help in diagnosis..
You can be advised scaling of the teeth to remove any 
plaque and 
tartar from the teeth..
Apply desensitizing toothpaste over the teeth and do a gentle 
massage for a few seconds and then brush teeth with it..
Massage the gums with antiseptic ointment..
Do antiseptic mouthwash gargles..
Chew a 
Vitamin C pellet daily to improve gum health..
Avoid intake of very hot or very cool foods and liquids and consume after cooling them to room temperature..
Hope this information helps..
Thanks and regards.
Dr.Honey Nandwani Arora.