Private practitioner Doctor Paul Gallop replies: Firstly, there is no evidence that wisdom teeth push other teeth forwards, this overlapping can occur as you get older because your teeth drift forwards naturally. So taking wisdom teeth out for that reason is not a consideration.
The pain you are experiencing is most probably due to food becoming lodged between the wisdom teeth and the tooth in front of it. One problem with wisdom teeth is there often isn't enough room in the mouth for them to grow fully. Partially erupted wisdom teeth have a loose bit of gum over them where stray food pieces can become stuck. This can cause decay and eventually the tooth to rot.
If you don't want to have your wisdom teeth out, you should make sure you visit the dentist regularly. Aim to have your wisdom teeth X-rayed every couple of years to check they're still healthy.