My gum is hurting and I have a feeling it is because my wisdom tooth is coming?

See your dentist. It is possible that your wisdom tooth is erupting. It is also possible that there is another problem. See your dentist to get a defiinitive diagnosis.
Consult. See a local dentist to determine whether or not the cause of your pain is related to an erupting wisdom tooth and what treatment, if any, is recommended. A one on one clinical examination and x-ray(s) are required to determine this.
Evaluate by DDS. If your dentist feels it is needed, you may be referred to an oral surgeon for further evaluation and possible third molar evaluation. Most wisdom tooth issues are addressed between age 18 and 21. It is possible that the pain that you feel is emerging third molars and they are coming in correctly.
Possibly. But 16 is a little early for wisdom tooth eruption. Would be prudent to have your Dentist take a look. Call him/her now.