I would argue there is a semantic difference between the two.
Tired means you need sleep whether you are inclined to or not (for example I can be tired but have insomnia)
Sleepy means you are inclined to sleep whether you need it or not (for example I am sleepy when I just get up in the morning)
However, I agree that the nuance is probably impossible to be shown in a post, so an alias probably isn't a bad idea. (Sort of like fear and scared from forum #16962)