Yes, the thyroid problems may cause the redness of the eyes. It may be the pink eyes which should be contagious. Since you have the thyroid problems, the immune system in the body will be decreased. The eyes may easily get the bacterium which may cause the eyes to get pink eyes. Or the dry eyes may cause it too. The redness of the eyes are just caused from the dryness. You should eat more food with vitamin C and A to moisture the eyes. If you get the pink eyes, you'd better treat them carefully. There are many reasons to cause the thyroid problems. The first reason is the iodine intake. Either too high or too low amount of iodine intake will cause the thyroid problems. The second one is the uneven diet. Most patients tend to be pay attention to the intake of food with high quantity of heat. They have neglected the fruits and vegetables intake. The third main cause is the unbalance in the psychology. The pressure and bad mood can not only affect appetite sleep but also affect the immune function and body health which will easily cause the thyroid problems. The last cause is the trauma infection, trauma car accident hurt and a cold which are likely to cause body infection disease and cause thyroid problems. Thus, you'd better have a good rest for the body and eyes. Treating the thyroid problems is the first task to stop the eye problems.
I have a friend once got red eyes and her recover section last so long then I accompanied her to the hospital, the doctor told us the redness is a sign of irritation. This can be due to dry eyes, allergies, infection, or inflammation, and can range from mild to severe.
In addition, thyroid disease can also be linked to dryness, and chronic red eyes. Other more rare causes would include some of the autoimmune diseases such as Lupus or Rheumatoid Disease.
I suggest that you take blood tests to confirm these problems, and sometimes treatment of the entire body is needed, with the red eyes resolving at the same time.
The reason for you may be dry eye, blepharitis or allergies, but if you have concerns, or if eye drops are failing to help, just go to see a doctor.