Pneumonia is not a specific disease, but is an irritated condition of the lungs resulting from any of various causative agents, usually a bacterial or viral infection, but can also be caused by a fungus or even a parasite.
You should check with your physician or other qualified medical person, regarding specific activities that might (or might not) worsen the condition.
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I suppose you could if you felt up to it, but you would be potentially infecting other pool goers. Walking pneumonia is contagious.