For I know that there is no direct connection between hypothyroidism and red eyes. There are many problems can cause red eyes. Such as pet dander, sun exposure, lack of sleep, eye infections, and some disease also can cause red eyes. If you get red eyes when you suffer hypothyroidism, tell it to your doctor for help.
Yes, hypothyroidism will cause your red eyes because of the interlinked eyes nerves. You will feel itchy at the eyes. You need to use some eye drops with anti-inflammation to make your eyes be moisture and comfortable. You could also do the medicine with anti-inflammation role to cure the hypothyroidism. Your red eyes could also be released through the warm compress which you could have a try.