The Wound Innovation Institute will research wounds and develop new treatments to manage them.
The windmill's cap and fantail assembly, which weighs about 10 tonnes, was removed to allow for repair work to be carried out.
Hull University Teaching Hospitals said people should buy common medicines like aspirin from shops.
Interim chief executive Lyn Simpson was brought in by NHS England last summer to fix issues.
Lilli Hales, 21, says she learnt to "just keep going" before she was given the all-clear in March.
Residents say their estate has been plagued by people parking to use Castle Hill Hospital near Hull.
The heath secretary says he aims to improve the trust that runs hospitals in Hull and Cottingham.
The world-famous silverware will be on display at pubs in Hull and Cottingham.
A total of 673 eggs have been shared with the region's hospitals and community groups.
