Zyrtec would definitely be the best option for you. It is available without a prescription and there are generic versions available that will be cheaper than the brand name (the active ingredient is Cetirizine so check the label on the generics to make sure that's what you're buying).
In order for it to help you'll need to take it every day since it sounds like you're around the dogs a lot. If you wait to take it when you're having symptoms it won't help as much.
You might also consider putting a room HEPA air filter in your bedroom and trying to keep the bedroom clean of any dog hair - there's only so much the meds can do if you're constantly exposed to allergens.