Given your health profile and the observations shared, the first step should be to undergo comprehensive blood tests.

These tests should include a complete thyroid panel (TSH, Free T4, Free T3, Reverse T3, and thyroid antibodies) to closely monitor your hypothyroidism.
Additionally, checking for vitamin D levels, B12, iron, and a complete blood count (CBC) could provide insights into your dry skin and depression symptoms.

Understanding these levels can help tailor your treatment more effectively.

Based on the results of your comprehensive blood tests, there might be a need to adjust your Thyroxine dosage.

Since you're currently on 50 micrograms and still experiencing symptoms of hypothyroidism like dry skin, an adjustment could significantly improve your thyroid function and, consequently, your general health and mood.
It's crucial to do this under close supervision to avoid overcorrection, which could lead to hyperthyroidism.

Engaging in a structured exercise program could significantly impact your depression and general health.

Exercise is known to improve mood, increase energy levels, and help manage weight, which is particularly important for managing hypothyroidism.
Starting with low-impact activities like walking, swimming, or yoga, and gradually increasing intensity could make this sustainable. Setting specific, achievable goals within this program can also provide a sense of accomplishment, further aiding in reducing depression.