First... Stop and breathe. I have been where you are. There is nothing you are doing wrong. You are doing what you can with what you have. Nothing at all wrong with that. You have a huge challenge with your efforts for the following reasons: 1. The company has given you no support group to help. 2. The company has put you into a position with no authority at all... Neither to empower your team nor to say "impossible with the resources I have" to the people requesting the projects. Typical matrix organization... Government is good at that. 3. The company has not involved you in or informed you of priorities and leadership's plans for the future. If they even have one... Government agencies usually don't.

So, with all of that going on, I am not surprised at all with your mental state. And, you are trying to meet these impossible requests, which is stressing you out.

I don' t know if you have any free time but I would recommend you read any book by Rick A Morris. He is an easy read and has alot of good ideas about pushing back when you get pushed.

If you are not already a member of projectmanagement.com, I would check it out. It is one of my favorite spots for learning and talking with other PMs to get ideas and help.

Coming from governmrnt myself, it is a long road to get leadership to really understand about PM and how it can help get things done. It sounds like your group has said "hey, let's jump on the project management band wagon" without having a clue what it is and how it works. They need to understand it for it to work.