Losing fur and sore on nose... Help!

My sweet girl Dutchess has been losing hair around her eyes and down the spine of her back... Both of my cats have been treated for fleas and I'm sure that isn't the cause. This weekend she developed a sore on the side of her nose. ( see picture ) she also has a growth on her bottom lip which she has had since I rescued her but it has recently started to grow and is now the size of a peanut. Dutchess is 12 and still has an appetite and energy - but has started to look sickly in the past few weeks can anyone help?

How old is she?

If she has a growth that is expanding, you should really take her to a vet.  It could be benign, but still in need of removal. 

I have no idea what would cause the type of hair loss you are describing, but it's possible that her body is using all its resources to fight the growth... and losing that battle.