There are many things you can do, and vacuming with a vacum that has air filters can make a big difference, if you can vacum and dust every day then do it!
When you groom you cat, can you do it outside? That will also cut down extremely on loose fur and it's dander.
There are sprays and whipes (like wet ones) you can use on your cat for allergies, there are spays such as the new Frebreeze spray you can use on furniture and carpets etc which is for pet allergies.
You can get other air filters which plug in, such as the True Air, or Ionic Breeze.
I would not recommend bathing your cat anymore then once a month, preferably every 2-3 months however. And using a CAT specific shampoo, not one for humans or dogs. Or one for a kitten if you have a young cat.
Keep your home well ventilated, keep doors/windows open when you can, a cross breeze would be great. Make sure the air filters in your house say clean!
If your boyfriend stays the night, try and keep the cats out of your bedroom, or off your bed, so he wont have to snuggle with a pillow covered in cat fur next to his face all night!
And yes, talk to him about an allergy medication.
There is hope, some people over time can build up a tolerance to cats, and for some lucky ones the allergy goes away all together!