M.B.
High cholesterol is correlated with being low thyroid. If you're taking replacement thyroid hormone (e.g., Synthroid, Levoxyl, Levothroid, Armour and/or Cytomel), you likely are under-dosed. There is a Texas Yahoo group where folks share their labs and experiences:
http://health.groups.yahoo.com/group/Texas_Thyroid_Groups/
Many people that are hypo are highly under-medicated. Most mainstream doctors unfortunately treat based on labs and not symptoms (e.g., your high cholesterol is a symptom of low thyroid). Also, that diet is likely to make things worse as your body does need cholesterol to produce hormones because it will limit things like beef, etc. And, many of these foods are important to maintain healthy iron levels. And, iron is really important for thyroid function - it helps get the hormone into the tissue since it can increase the amount of red blood cells in your body.
Also, given your son's mild autism, you may well have genes that pre-dispose you (due to genes) to having problems detoxifying - the detox pathways are often "broken" in folks with autism. An overload of toxins really interferes with normal thyroid function and thus you may need a supra-physiological amount of thyroid hormone for issues to resolve. Few doctors will Rx that, so you may need to find a new doctor. Again, the Texas Thyroid Yahoo group is good for that. Tell them MaryB sent you as they do control membership to avoid SPAM and to avoid lurkers that have intentions to undermine the effectiveness of the group.
Note that I'm not a medical professional - just a patient advocate. I had to be extremely aggressive to get thyroid treatment that helped my symptoms resolve and I feel that it's really important that I share my experiences and knowledge so that others will get the healthcare they need for their thyroid - it controls many, many processes in your body and it will stress just about every other system if you're not properly medicated. I too had high cholesterol at a very young age and many other symptoms of low thyroid over the years. My cholesterol is now in a very healthy range and I eat a diet very high in healthy fats, including red meat several times a week as well as LOTS of nuts and seeds.