I've been allergic to cats all my life, and have always
had cats regardless what doctors told me.

What helped me most was;
1. getting allergy shots (which you should do regardless)
2. washing my hands after touching cats
3. having a deviated septum fixed (a nose job)

Aside: all cats are not equal in the amount of allergens
they produce from their saliva.

If you have money...
post an ad in the local newspaper.

If you haven't much money...
Print out and post an ad to put at supermarkets, laundry mats,
and/or other places to find them a home they can live, and tell
the landlord to give you just a few extra days to find them a home.

If worse comes to worse...
find a no-kill animal shelter nearby they can go to.

Do your best to find them a home, and
thank you for caring.