Popcorn, I know how you feel.
When I was your age I couldn't have a cat in the house because my dad was too allergic.
What I did to get my kitty fix then was to petsit for my neighbor's cat.
Maybe you could make an offer to petsit for this neighbor or others that own cats near you.
Now I take my kids to the shelter to visit and socialize with the cats and sometimes take a dog out for a walk.
Maybe you could volunteer at your local shelter so you can play with some cats there.
I took my daughter there for an hour last Saturday and we had so much fun playing with some of the cats.
Here is my favorite, a perfect little tuxedo girl named Cookie, a total lovebug.
Cookie
I also played with Kansas, a cute black cat with a little white on his chest who keeps telling me that he belongs in Ohio with Cataholic.
You really should petsit or visit your shelter and enjoy spending some time with cats.
When you are ready to adopt a cat of your own you may find that an older cat like Samantha will get along with your birdies just fine.