Introvert here in a small MSP with a catch all position from server herder to desktop trenches.
Working with users is important. You NEED to have the soft touch when you need it. When a 50 year old loses a familiar site, it can be MAJOR for them. They've spent decades building an efficient work flow around certain pillars. What works best is: the post it! Something they can slap on their monitor or cube wall with "translations." Taking the time to explain to them the changes, why and how etc, will reassure them, and the cheat sheet will make them understand you care. They'll be upset for a few weeks, but in the long run it forces them to learn.
I would suggest implementing a ticketing system. If someone asks for something, tell them to put in a ticket. My favorite response is "you caught me right in the middle of something, if you put in a ticket I'll get to it as soon as I'm done with this in 15 minutes." Which is usually true. If someone comes in and demands something like the CEO's brother, have a backbone. Don't be afraid to say no, or put in a ticket etc.
Monitoring your infrastructure is also good, especially if it's mission critical 24/7, which it sounds like it is. It can be as easy as setting up a junk server, pinging gateway/objects every five minutes, and if it's down, shooting off an email.
If people are coming to you for the same thing over and over, you should either implement training, or a knowledgebase. Working to reduce your workload via automation, or documentation is a MUST.
As for communication, that's really important. Don't rely on secretaries or receptionists. If something is down, they're usually inundated just like you. I'd suggest a free chat system, like openfire and pidgin, that you dump onto a few workstations for emergency communications. Redundancy :D
Besides all of that, I would suggest a meditative method called mindfulness. If you stop, list out what's bothering you, taking a few deep breathes, correcting your posture and relaxing your shoulders 8-10 times a day, it does WONDERS. Try it for a week or two. That or go for two 15 minute walks if it's nice out. It can help you sort out info, and put things into perspective. It can also give you some inspiration. If you're still overwhelmed after making changes, advocate for yourself. If you need another team member, ask for one. If you see tech that can help automate or provide failover, ask for it. Then document it.
It's gonna be okay man. I know sometimes users get you down, but sheeeeeeeeeit man, you can't let them get to you.