the only thing I can even think of . . . you just took methotrexate right? One of its side effects is making the blood more likely to clot. Are you having any pain? like in your lungs/shoulders? If you had a blood clot in your lungs I would think that it would HURT alot (and you would probably cough up some blood). If this is the case at all I would definitely get in to the ER!
I know what you mean about a sore throat afterward. those tubes suck! I ususally have a sore throat for 3 - 4 days afterward. I find eating Nutella straight off the spoon works pretty well.

But I've never coughed up blood from that
Hope it's nothing and you're okay!!!