If you couldn't tell, it's my first day in the hospital.
("I" had a terrible day in the hospital that day.)
Does this underlined phrase mean "I think you can't believe it" or something?
1. If you can't tell, it's my first day in the hospital.
2. If you couldn't tell, it was my first day in the hospital.
It means something like "In case you don't/didn't realise ..."
"Tell" in this case means to realise, to discern, to understand, to infer.
"I couldn't tell you were American" = I didn't know just from looking at you that you were American, and there was no other evidence to make me think you were."