You're speaking with Dr. Michael Salkin. Welcome to JustAnswer. I'm currently typing up my reply.
Colin, the most common cause of Cleo's sneezing and epiphora (watery eyes) is infection by the feline herpesvirus (FHV-1). Most cats are carriers of this virus which can come out of its carrier state in times of stress - such as moving house. Thankfully, most cats remiss unaided within 1-3 weeks and so I rarely treat them. When symptoms persist longer than 3 weeks or my patient worsens instead of improves over that time frame, I consider administering an antiviral drug such as famciclovir.
Sticky fur indicates lack of grooming which is consistent in any cat under the weather. I must assume that her odor is also due to her not cleaning herself as she does when well. Please respond with further questions or concerns if you wish.
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