I had four teeth extracted in the past week. is it normal for the surrounding teeth to be sensitive and a little wiggly. ?

Yes it would be: Sounds like you have had major oral surgery and it is not surprising your mouth is tender and teeth feel a bit wiggly. It should get better over time but if is not call the doctor who did the surgery to discuss it with them.

Not unusual: Assuming at 16 that it was your wisdom teeth were removed. Surrounding tissues become inflamed in response to the surgery, resulting in some instability of the adjacent teeth. Expect adjacent tissues, bone, gums, and teeth, to be somewhat sensitive. Remember, it was surgery, and will take time to heal. If you are concerned, check in with the Dentist or specialist Oral Surgeon for review.