Are you noticing any changes when you are taking the steroids? It can affect how the thyroxine is converted to T3 but I couldn't say for sure. It might actually help in cases where cortisol levels are low. What you may find is that when you stop the steroid treatment, it might take a little while for your cortisol levels to get back up to normal (which is why it is important not to stop taking steroids suddenly). If this happens it can make you feel pretty awful and can result in inadequate conversion of thyroxine to the active T3. This is usually temporary and the adrenal glands do eventually kick back in.
Obviously you need to take the steriods for your lung conditions and shouldn't stop without the guidance of your doctor, but it could be affecting the way your body handles thyroxine on a short-term basis.
I expect someone else will have more information.
I hope you feel better soon. It sounds like you have a lot to deal with at the moment!