1.Increasing
thyroid replacement is not only based on
TSH levels. We also need to look at other signs of hypothyroidism like severe dry skin, tiredness, weight gain, hairloss etc. Also we need to check on the FT4 levels. If that is normal you may not need to increase your replacement.
2. With respect to hypothyroidism and eczema it could be a common autoimmune condition that is triggering both the conditions.
Next Steps
Check for auto antibodies for Hashimotos thyroiditis
Health Tips
Take an anti-inflammatory diet. Most commonly gluten, dairy products trigger inflammation (not for everyone - can avoid and see). Avoid stress and adequate sleep