There can be a link between hypothyroidism and high cholesterol. Your thyroid hormone levels most likely need to be changed. Actually 12.1 is more than twice what is normal. 6 is now considered hypothyroid. A few years ago, the standards were changed to normal being closer to between .3 and 3, although some labs still take numbers higher than that as "normal." I would consult your endocrinologist. Also, with a history of thyroid cancer, you should be kept on the low side of TSH anyway, even after so long. You may not need to be suppressed as much as a newer case, but on the high side of normal probably isn't where they would want you. I would talk to an endocrinologist with experience treating thyroid cancer patients about this. It's not necessarily the same as treating a regular hypothyroid patient and many regular physicians may not know the difference.
Even after your TSH is in the normal range, however, you may still need to be on a cholesterol lowering medication. Diet isn't always the problem. Genetics plays a big part in high cholesterol, too. Also, it's what kind of fat you eat, not just how much. Good fats, like avocado, nuts, olive and canola oil, and cold water fish all have good fats, which help raise good cholesterol. This is something you need to talk to your doctor about. Cholesterol lowering medications may just be inevitable, even with a normal TSH and weight.
Once your doctor does increase your thyroxine, go back in 2-3 months and get a follow-up blood test to check your TSH. I don't know how long it takes to effect your cholesterol, that's something you'll have to discuss with your endo.
Best of luck. Let us know what happens. You might help the next person who comes along with your same problem.