Yes. Wisdom teeth erupting can cause temporary soreness, and the gum flap over a partly erupted wisdom tooth can become inflamed, a condition called pericoronitis, which often settles with cleaning, warm salt water rinses and, where needed, treatment at the practice.
Not every painful wisdom tooth has to come out.
Removal is considered when episodes recur, when the tooth is decayed or damaging the tooth in front, when there is a cyst, or when it cannot be cleaned adequately.
An X-ray shows the position and root shape, which determines both whether removal is advisable and how involved it would be.
Where the tooth can be kept and monitored, that option is discussed.