Does you cat have the same thing as you or are you just worried because they are a pet? As long as you are being sanitary I wouldn't worry about the cat if they are not infected. I sent mine to live with a friend until I got better though.
A liver detox you want to do in the end. You should stick to the order the outline //www.curezone.org/cleanse/.
There is a systematic reason for it. Cleansing in arbitrary order just might make things worse. Also, you are not going to get better over night. A good parasite
cleanse that I used was paramax/paragone. They sell it online as paramax and at wholefoods as paragone.
As for seeing more instant relief, the fastest way is a change in diet. Low suger, low carbs, 50% protein, high fiber, and watch your gluten. Also cut out as many toxins are you can such as caffeine, alcohol, and cigs. Just getting familiar with an anticandida diet is a quick reference. parasites
also like carbs though; gluten or no gluten. Therefore watch the rice, etc. Don't cut something completely out of your diet though that you need. It will probably hurt you more than the problem. You might feel worse at first, but it will clear up. Especially if you are not much of a fiber eater. When I first switched to a higher fiber diet, I was freaking out because I had a lot of gas.
If you are completely overwhelmed, I would honestly find a naturopath in your area which is familiar with the problem. It might cost money out of your pocket but it is better than throwing your money at random things not knowing what you are doing. Use the internet and chatgroups as a second resource.