Should I take thyroid medication if my TSH is 4.22 and I feel sluggish and brainfog and anxiety and depression?

Yes. If you have been prescribed synthroid (thyroxine) for hypothyroidism (or subclinical hypothyroidism), take it. Hypothyroidism may cause you to feel depressed and an anti-depressant would be ineffective if your thyroid problem isn't addressed. A TSH of 4.22 suggests hypothyroidism, but is a borderline value and may not be full story. See your doctor for a full work-up.
No. Though thyroid hormone replacement may improve your symptoms, you TSH isn't high enough to justify blaming your symptoms on an underactive thyroid gland. You should talk to your doctor to determine if you are experiencing side effects of other medication, have nutritional deficiencies or maybe suffer from sleep apnea. And depending on your age, several other abnormalities can lead to your symptoms.