If tsh level is 4.5 with thyroid nodules could that be reason my hair is falling out, dry skin and dry eye?

Possible: But your thyroid level really isn't low enough to cause these symptoms. See you doctor about brand name T4 replacement to normalize your tsp. Thyroid nodules are a separate issue and need other evaluation.

See an endocrinologi: Your TSH is slightly high. As people get older they tend to have higher TSH but may not have low thyroid. It is not certain if there is benefit to taking thyroid pills for this. You need also to determine if the nodules are malignant. If you take thyroid, the generic is cheaper and just as effective. An endocrinologist is what you need.