Your orthodontist has asked you to wear elastics. This means that, on top of the pull from the archwires, the teeth you hook the elastics onto are also receiving this extra force. It is normal for them to become more sensitive for a while. The more you wear your elastics, the faster your teeth get used to them and the discomfort stops. If you often take breaks from your elastics, you may feel discomfort every time you put them back in. So wear your elastics as your orthodontist has instructed.
This answer is for general information. Your own case needs an examination by an orthodontist.