Hospitals
Prior to the 19th Century there seem to have been no hospital facilities in Rotherham. Medical treatment was not free and most doctors and surgeons charged a great deal. Some of my history reading indicates that fees could be as much as 5 guineas a visit: an impossible sum of money for anybody but the very well-off. An ill or injured person would have to be looked after by his family and maybe the local woman who did a bit of nursing. Advice, together with medicines, most often came from the apothecary, if you could afford it. Victims of epidemics were often isolated in huts well away from the town and looked after by elderly women with little to lose, though to call them nurses was probably a gross exaggeration.
Doncaster Gate Hospital
The increasing number of industrial accidents in the works and factories of Rotherham led to a demands for a hospital. In 1867 a fund-raising committee was established and the sum of £1000 was received from Miss Elizabeth Nightingale, towards the projected costs of £6000. Doncaster Gate Hospital was opened in 1872.

It was a magnificent building (still is) in a four acre site close to the centre of town. For a lot of information about Doncaster Gate Hospital visit www.doncastergateheritage.org.uk.
Rotherham Workhouse
There was also a hospital in Rotherham Workhouse but I believe that, during the 19th Century, this was for the treatment of the pauper inmates only.
The Fever Hospital
Cholera, typhus and other fevers were the great bane of the early 19th Century but were brought under some degree of control by the advances in water supply and sanitation. Tuberculosis continued to be a great killer especially in the crowded tenements, and smallpox, scarlet fever, measles, German measles and mumps all took their toll. In 1887 a Fever Hospital was established well outside the extent of Rotherham on Badsley Moor Lane.
The Rotherham Dispensary
The Rotherham Dispensary was founded in 1806 to treat accident victims within one mile of the parish church. It originally had premises on Wellgate but in 1828 moved into a building in College Street which was erected on the site of the Town Hall. Casualties were treated in situ but patients requiring hospitalisation had to be sent to Sheffield.