I'm 20 and have a tooth coming in ?

Hi, I'm 20 years old and for the past few months. I have had swelling that would switch from left to right around the last tooth on each side in my mouth never at the same time(hurt like H e ll too!). I started having this white growth, I noticed on one side a few months ago. Now I realize it's a "tooth" it cause's pain in a few of my other teeth around it (it looks like it has no room to grow).Is it normal at my age to have a new tooth coming in when I did not lose one? I don't know nothing about molers or wisdom teeth, I'v been to the dentist once in my life . I appreciate any advice or answers Thanks,Heather