Red droplets coming out of male cat's privates, vomiting, pain, low meow

My male cat (1 year old now, was fixed when he was a young kitten) is meowing low and loud and sounds like he's in pain. He's licking his private area a lot. He threw up a lot at once, probably half his food bowl. The vomit didnt have any objects or whole kibble in it, it was the texture of chunky oatmeal. His chest/stomach is occasionally twitching and it's synchronized with when he clenches his private area. He looks like he sucks his penis and butt closed, clenching, but then when he opens it back up, there's a small droplet of red liquid that came out of his penis. Definitely not coming out of his butt. The liquid is stinky and it when put on a paper towel, it is mostly clear with just a hint of red. I have him on a white cloth right now so I can see how much comes out, and in the past 2 hours it's only been a few droplets. He hasn't used the litter box or drank water in the past few hours. He's just resting now but occasionally like once every half an hour, let's out another low meow. I have called the vet but they weren't able to see him today. Is this an emergency? Should I bring him to an emergency vet? What could be wrong with my cat?  

Hello!  This sounds like a potential  emergency.  Please call the emergency vet for triage and further advice.   I will answer fully later !

Hello!  This sounds like a potential  emergency.  Please call the emergency vet for triage and further advice.   I will answer fully later !

Hello!  This sounds like a potential  emergency.  Please call the emergency vet for triage and further advice.   I will answer fully later !

Just an update - I took him to the emergency vet and they are sedating him, giving him a catheter, getting rid of the blockage, running tests, giving IV and painkillers, and keeping him there for 8 hours. Thank you for your response Liz, I was having trouble determining if it was something that would pass on its own or if it was an emergency. It turns out taking him to the vet was the right choice! She told me it would have been bad if he didn't come in today.

I'm so glad - was thinking about him!  Wishing you all the best from here