I have severe chest pain around my sternum which is worse when lying down and trying to move around. What could this be?

Go to the ER. Severe chest pain should never be taken lightly. The positional nature of the chest pain makes one think of a possible pericarditis (inflammation or infection of the lining around the heart) although this could be a heart attack, blood clot, lung infection, etc. All possibilities that are very serious and should be excluded rapidly. Especially because you are on an immunosuppressive. Go now!