That is a great question. Stress causes changes in the body's normal physiology that can be beneficial (think fight or flight response) but long term exposure can lead to negative side effects such as chronic fatigue, depression and weight loss
or weight gain. Rashes can form because of long term stress issues. It is possible that stress is indeed the cause of your mother's rashes. On the other hand, living a stressful life in the hospital can bring about rashes from a variety of other causes. This can include communicable diseases and hygiene related issues that may be the underlying cause of her complaints. It would be prudent for her to be evaluated by her primary care doctor
who can best assess her medical history and presenting symptoms and decide upon the appropriate work up and treatment options if available. Things to look for when observing rashes include whether they are tender, red, warm, enlarging, causing any associated complaints such as difficulty breathing, if they feel like they have an underlying fluid collection or if they are draining any fluid. If you notice any of these issues, it is important to be evaluated by a medical professional as soon as possible.