My current tenant has complained about an allergy - I have mold allergies too - and I do want to make sure I have a healthy place for tenants to live.Do I sell or do I keep it?

Replacing carpet with anything other than carpet can make it more friendly to tenants with allergies.  

Some people can have a severe allergy to a certain type of mold that doesn't bother anyone else. 

Are you rejecting the animal because you have a severe allergy and would be unable to visit the home to collect rent or inspect the property, or maybe you were attacked by an animal as a child and you have a diagnoseable fear of dogs.  

We state a person with a cat allergy should be able to rent the apartment with no ill effects.

Dogs would be a problem because of allergies, but they're ok with cats.If you have any contacts who might be able to help her find something, please pass on my email. 

Duct cleaning is to help with allergies, but its a waste of money to resolve improper temperature or other HVAC performance issues.

The issue hasn’t so much been the smell, more that there’s an allergy in our family to incense smoke.

Which will make it much easier in the future to accept when I enforce the lease to the letter on future occurrences.For example, I just paid to have duct work cleaned at a rental property because the tenant was complaining of allergies and possible mold in ducts in an older house - but I didn't have to. 

Your next tenant might have allergies.