My 2-month-old cat has watery eyes with discharge, occasional sneezing, and constantly makes a rumbling purr-like sound

Generally, when a cat purrs while eating, drinking, and using the litter normally, it shows comfort and pleasure. Some cats purr when relaxed, being affectionate, or in heat, also seeking attention. However, if the cat purrs for a long time and, as you describe, has watery eyes and sneezing, it is very likely a respiratory infection or nasal blockage.

Watery eyes, eye discharge, and occasional sneezing may be the body clearing pathogens. The rumbling sound may come from some degree of airway blockage or inflammation. It is recommended to take the cat to a veterinary hospital for respiratory screening and imaging, and to treat the symptoms actively.