Can wisdom tooth extraction make you feel sick?

YES: The feeling should only be temporary and is usually due to the ingestion of blood or the more likely the pain meds you are taking.

Possible : Not sure what you mean by "feel sick". The removal of wisdom teeth is a surgical procedure and it takes time to feel "normal" again. If any type of IV anesthesia was used it can take time for that to leave your system. You probably are not eating and drinking normally so you can become weak and dehydrated from that. Meds you are taking can also affect how you feel.Also you may have caught a bug.

Yes: So much in dental treatment depends on the patient, their pain tolerance as well as the type of extraction, ie; bony, or ankylosed. A surgeon's skill, touch & the way they do a surgery. Great hands with a patient who follows all of the home care directions can lead to a very positive result with very little pain. With all the variables, pain could be minimal or could last weeks. Meds can help.