Can my bottom front teeth hurt from wisdom teeth coming in or pushing on the molars?

Referred Pain. It is always possible to get some referred pain in the head and neck region, but without radiographs and an examination, one cannot say for sure this is the cause. Calculus deposits behind your front teeth causing inflammation, and grinding are two other possiblilites. Have your local dentist take a look.
In my opinion. Although this was thought to be true years ago and may still be a controversial subject, my answer to that question would be rare if at all. Look fir other causes.
Possible but. It is possible that erupting wisdom teeth can effect your front teeth, but there are many more likely reasons for your front teeth to have pain. The only way to know what is going on in your mouth is to see a dentist. Do not ignore this. Get checked.
Definitely, yes. The most common complaint associated with impacted wisdom teeth is pain. It is not unusual that a patient may have soreness or pain in the back part of the jaw, ear ache, sore throat or pain in the side of the face. It's called heterotopic pain.
Yes. Yes. Seek an evaluation. For best results with wisdom teeth, make sure you are evaluated and treated by a board certified oral & maxillofacial surgeon.