I don't know if this helps, but I am also allergic to all kind of things, including pet hair, yet have 4 indoor cats. There is a huge amount of hair inside my house, yet I need a good vacuum cleaner. I now use a bagless vacuum cleaner, so I won't have to clean the bag after cleaning all my house. There are plenty good bagless vacuum cleaners on the market. I have never though about
dryer sheets, but will try in the future with another vacuum cleaner.
Also, do you have a vacuum with HEPA filter to get rid of odor while cleaning? Here are some good vacuums with HEPA filters.
@auntlucy what do you mean about tablets to put in the bag (at Hoover?). Thanks!