Pains on left side of head from temple to eye symptoms have occurred for a month and have gotten more persistent. And past couple of days I have been getting dizzy when pains occur. Should I be concerned?

Probably not. You should have a doctor check you out but this is probably not a serious condition. You may be having irritation of a nerve in the face or a muscle spasm in the temple. Another possibility is some TMJ syndrome causing pain in the face / temple area. If you have worsening, more frequent pain, sudden hearing loss or numbness / tingling in the face, see the doctor right away.
Any new headache . Should be assessed by a primary care physician and if needed, referred to a specialist. First a history and physical exam need to be performed. That is the starting point for any medical assessment. Once there is a working diagnosis, tests might be needed or perhaps a trial of medication. At your age of 16 the landscape is different from a 51 year old. See pediatrics and get this checked.