I agree with Marz and Grey Goose. read Dr Kendrick's books or google to find his blog. What is the real cause of Heart disease. 29 parts and counting. He is a practising GP with a specialism in Cardiology and has been advisor to the European Board of Cardiology and consultant for NICE re cardiology info, so to be respected.
Also go to Chris Masterjohn's facebook page or google for website. He is the researcher of researchers - does the research so you do not have to! He has hypercholesterolemia himself (sorry if that is spelt wrongly) he has lots of informative videos on his facebook page. Has done many this year, one definitely on hypercholesterolemia. Lots of data, facts and figures and research and answers your questions. At least on relatively new posts. He has answered mine. So full of respect for him and his work. Look up his 'Vitamin K2 Resource' guidelines - nothing else out there like it. You will see what I mean. He tackles everything to do with nutrition and is a total expert on fat soluble vitamins and chloesterol.
I heard Dr Harpham (Cambridge) speaking many yrs ago. Of how her colleague was at the European conference re cholesterol and statin introduction. Discussion included, what the level of cholesterol should be set, at which guidelines state Statins should be prescribed. There was much controversy - average cholesterol level about 7-7.5. This colleague during recess for lunch/ break overheard the discussion between 2 decision making panellists. One stated to the other that a decision at a figure of anything above 5 would mean that not enough people would be drawn into the net of target statin prescribing. She had no doubt after eves dropping on their conversation that what figure would be determined on to create policy. So A) just a made up figure with no evidential research behind it and B) determined on from self interest of pharmaceutical company/s involved in research and production.
You need to read Dr Kendrick's book 'Doctoring Data' fascinating and informative and I feel you will never look at our medical system the same again once having read.
Research proves no benefit to women ever, in taking a statin.
The reason, cholesterol can go up when hypothyroid is because the thyroid hormone is responsible for the functional pathway of creating LDL receptors on every cell. If you do not have enough receptors on cells, the LDL shipments cannot dock at the receptor and deposit it's load of cholesterol into the cell. So because of lack of receptors, your LDL particles will be left hanging about in the blood (just ready for your blood test) It obviously is not good for LDL particles to be left hanging about in the blood because they are then exposed to oxidative damage but the answer is not to use a statin but to sort out the root cause of the problem and that looks like hypothyroidism in your case as you presumeably have been diagnosed.
You could also look at why you have an underactive thyroid. And try and achieve as many positive approaches to help your thyroid as possible. Receptors for iodine on the thyroid cells are going to be occupied and blocked to receiving iodine by other sructurally similar halogens such as bromine (fire retardents in your mattress/furniture) chlorine (in tap and bottled water/ swimming pools. But absorb mostly from the steam in a shower) fluorine (fluoride/toothpaste).
Note: cholesterol levels fluctuate through the day, they do not remain static. LDL is so critical it is part of the arsenal of a functioning immune system. If your body detects it is under threat from pathogens then LDL will be held back in the blood to help neutralise the threat. If this is an ongoing threat, then LDL is going to be found high in the blood always. Is the answer a statin! No way is that going to help - working agains the body!
Also cholesterol levels need to be much higher as we age. Probably because function has been compromised over the years or more infections over the years have established their homes, hiding in biofilms of your own cells. What ever the reason is we need a higher cholesterol as we age, the body is trying it's utmost to keep us alive and does not work puposely against us.
If you believe any hypocholesterolemia is due to a genetic defect then I believe it would be prudent to be tested for the genes first to see if you carry them before resorting to a statin which has no positive endorsement in research for women.
And with the emerging science of epigenetics (influences above the genes ) lifestyle factors and diet and a healthy balanced microbiome will play a huge role as to when/whether genes are switched on and off.
If you have all this info and research at your disposal, you will be in a far better place to influence consultant and your own decision making