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!