Welcome. HCM is actually not a consequence of hyperthyroidism or hypertension; people say this but it is a 'lazy' explanation ;-) HCM causes a particular chamber of the heart to become abnormally thick; hypertension and hyperthyroidism also cause this same chamber (the left ventricle) to thicken. So, HCM, hypertension, and hyperthyroidism all cause the same thing to be found on echo. (Note that not all cats with hyperthyroidism or hypertension have this; it is an unfortunate consequence in some cats who aren't treated or who are inadvertently under-treated.)
What does this mean? This means that cats with hypertension or hyperthyroidism have LV thickening as a secondary consequence, and it's possible to reverse it when these primary diseases are treated. Cats with HCM have a primary heart muscle disease. (You can tell the difference on autopsy, BTW, but who wants to think about that?)
Sooooo... since your cat had hypertension and hyperthyroidism that was not well controlled, she could have LV thickening or primary HCM, but no one can tell until those things have both been very well controlled for months. If she doesn't have HCM, you should probably see an improvement AFAIK. Has she had an echo by a board-certified cardiologist?
Re: asthma. You can use inhaled meds for cats with asthma, and these are generally not contraindicated for cats with heart disease (of course you have to discuss with your cat's cardiologist). Check out www.fritzthebrave.com for more info, should you need it. Keeping things as dust-free as possible in the home (check the ceiling fan blades--they are usually a wealth of dust!), not using incense or scented candles or sprays, etc. can help as some cats have a component of allergy to their asthma.
Hope this helps :)