What can cause a rash, achy joints, and lethargy in an otherwise active, healthy (5'7", 135lb) 16 year old female?

Viral infection. . .: An otherwise normal, healthy young person can get rash + joint aches + tiredness from problems such as: viral infections (including those caused by certain bug bites), allergic reactions, auto-immune conditions (like juvenile arthritis), and a few other disorders. It is time to see the primary care doctor, who can evaluate and help with the diagnosis.

Immune/autoimmune: This could be something like lupus, or arthritis, possibly could be a virus, definitely worth seeing your PCP as testing will be necessary to determine cause