If I said or typed “He’s pissy today” what would you think I meant? Please be specific, if possible.
I’d think that he was in a very grouchy mood, probably making snippy remarks to others for no good reason and otherwise taking it out on the world.
Yes.
I’d take that to mean someone was being more short-tempered than usual. Easily irritated, perhaps prone to making snide and/or sarcastic remarks.
I have those days. It can also be related to blood sugar issues for me, too.
That he’s in a foul, grumpy mood, usually for a reason unrelated to the speaker or interlocutor.
Grouchy, irritable, out-of-sorts - don’t bug him more than you have to today.
After you get enough feedback, are we going to get some juicy context? 
What they said.
Agreed.
What FH said.
I agree - more irritable than usual, acting somewhat jerkish.
Everyone has their bad days, but taking it out on others is a crappy thing to do. Obviously, you aren’t an automaton and you don’t have to be all smiles and giggles all the time, but depending on how pissy said person is, behavior like that is a luxury that teenagers and younger kids have, not adults.
What RNATB said.
Snippy, easily annoyed, and lashing out at people over small things.
Can we ask why?
Yeah, bitchy. Rather common term. One I use to describe myself quite often. 
Did someone think you meant the target of the sentence was incontinent, or drunk? (For the latter, using the British definition of the word “pissed.”)
In a tame argument with my boyfriend, I essentially claimed that I was often pissy and that he was never pissy, which led to a discussion about what exactly the definition of pissy might be, at which point I decided to survey dopers to how people define pissy. And you all agree with me.
Of course, then he comes into this thread and says something DIFFERENT about what constitutes pissy, so the argument is less tame now!
This.
Forgot to add: “pissy pants” is a fun variation on the term.
Example: “my my, aren’t we a pissy pants today??”
+1
Having read the other responses in this thread, I am now of the mind that the OP is, indeed, pissy.
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And now, for my next impression: Jesse Owens!