I woke up in the middle of the night with severe vertigo and was later diagnosed with strep throat, 7 days later I still have vertigo?

Vertigo. This should not be confused with "dizziness" and has specific definitions. If you feel yourself spinning around the environment or the environment around you, or you feel the ground is coming up to meet you when you look down this is vertigo, and often suggests inflammation of the labyrinth, the most common cause being viral or bacterial middle ear infection. See an ENT doctor.
Yes. Dizziness can be part of overall "feeling sick" with many illnesses. If it persists after resolution of strep, it may need to be investigated.