You are not a bad meowmy. You took your kitty to the vet, right? It's very normal for cats to grieve. It seems to be pretty common for one cat to become ill shortly after the other one passes. I'm not sure why that is, but I've heard several other people express the same situation. I'm guessing it's because cats are so good at hiding their illness normally, but they can't hold it together while they are grieving or something. Actually, it happens with people too--my grandmother fell apart after my grandfather died, as though she could finally admit she was ill too.
Anyhow, now that you know, hyperthyroidism is very treatable. The best possible treatment is the most expensive upfront (though it can save you money in the long run). It's called radioiodine treatment, also referred to as I-131 for the isotope of iodine that is used. It tends to be about $1000 to $1500 depending on your state. The cat stays in a special facility for several days (again the length depends on your state) until most of the radioiodine leaves the body. Some people are reluctant to go this route if their cat has other issues, such as kidney problems. However, not doing the procedure doesn't make kidney problems go away--it just means managing two illnesses at the same time. The best part of this option is that it offers a cure in most (about 95%) of the cases.
The second option, which is more commonly used, is medication. The medication is called Tapazole (generic: methimazole), and it can be bought at human pharmacies as well as from the vet. You can shop around to find the cheapest place and have your vet write a prescription. Some vets want to do a trial on methimazole before agreeing to refer you to an I-131 facility. There are cats who have done well on the medication for as long as 5 years, but the medication can be hard on the liver, and it is a treatment, not a cure. Blood tests need to be done periodically to verify that the medication is still keeping the thyroid levels in check, and sometimes adjustments need to be made.
The third option is surgery to remove the lobe of the thyroid. It is not recommended in most cases because even if one lobe is removed, the other may have a nodule as well. Also, the thyroid glands are very small and are attached to the even smaller parathyroid glands. If the parathyroid glands are damaged, the cat may end up hypercalcemic (the parathyroid glands regulate the calcium level in the blood). This is very dangerous. If you do choose the surgery route, be sure to find a surgeon who is very experienced in thyroid removal.
A few people have had success with homeopathic treatments, but there have been no long term studies proving their effectiveness, and many people have been very unsuccessful.
The final option is a very poor option, which is no treatment at all. Hyperthyroidism speeds up the cat's metabolism, which taxes all of their organs, especially the heart. It's not uncommon for hyperthyroid cats to have evidence of heart damage, usually cardiomyopathy, and heart murmurs. Sometimes they need treatment with heart medication; other times, the condition is mild enough to wait. An untreated hyperthyroid cat will become extremely thin and eventually starve to death because they cannot take in enough nutrients to keep powering their metabolism.
My hyperthyroid boy was Spot. I found him, age unknown, on September 7, 2004. He stayed with me until April 8, 2006. He was treated on methimazole, except for the times after we attempted I-131 (he was the extremely rare case that didn't respond to treatment). He did well on methimazole but had an underlying heart problem that eventually took him. I felt like a bad meowmy because I had forgotten to have his heart rechecked after the first one showed a problem and the vet recommended checking it again later. I know in my heart that I did the best I could for him, and I gave him a good life with me.
If you have any questions, feel free to ask here or send me a PM. When you get his test results (ask for a copy), would you post them?