Hi D.
I just wanted to tell you that you should not beat yourself up! Being a mom is a really hard job even in ideal circumstances and when things aren't always ideal, problems seem to magnify. It is hard to have your husband TDY a lot. Since I'm old enough to be your mother, I feel like I'm qualified to give you some advice, for what it's worth.
First, I know you like having the income your job brings you. However, if you really crunch the numbers, I think you would find that after taxes, and whatever you might end up having to pay out of pocket for your son's care while you're at work, it's quite possible you're only bringing home a few dollars/hour. Plus, taking care of kids is hard work. Especially with your husband beind TDY so much, it's possible that he's making a little more money with per diem. If you really worked on your budget, you might be able to find a way to stop working for a while.
Go to USAFE Services or Army Community Service (for all service members and dependents) and find out what kind of support services they have that you can take advantage of. For example, they might have free childcare program for students.
I strongly recommend that you find a way to continue your education either at a local university or online. There are tons of tuition grants available and you may not even have to pay up front. You should take some general education courses and figure out what types of things you're interested in.
If you feel like you need to contribute to the household income or help pay for your education, you could offer babysitting services on your own. I bet there are plenty of people who would not mind if you brought along your son and babysat their children so they could have some time out. Good babysitters are hard to find. This way, you would not have a set schedule and could work it around your classes and your son's needs.
I can't stress enough how investing in your education now will be a huge pay-off later. Your budget might be tight for a few years, but once you're finished you'll be qualified for job with good pay and benefits and it will all have been worth it.
Also, you could start a co-op group with other moms. You could use poker chips--red=one hour, blu=half hour (or whatever) You would each start with the same number of chips (say 20 hours worth) and you would use them to trade with each other. You just keep everyone on a list and call each other as needed. Just make a rule that no one can hold more than 35 hours worth at a time so that people aren't taken advantage of, and another rule that says each member has to say yes at least twice per month or something like that, so that no one gets away with not participating. Anyway, just an idea.
The point is, if you simplify your life a little, and get together with others to help each other out, you will feel less stressed about being all alone.
Now I'm going to get personal. You're young, and you see a lot of young people going out and having fun and doing things you can't because you're a mom. Here's the deal: it might seem fun to you because you don't get to do it often, so you think you're missing out. Consider this: Most of those people going out and "partying" are looking for love, "happiness" and some sort of a connection. Soon they will get very tired of that whole scene. And do you know what they'll start wishing for? A husband who loves and takes care of his family, a home, a child---in other words, everything that you already have. It's hard to see that now but trust me, it's the truth.
The other truth is, you have made the choice to be a wife and mother at a very young age--that was your choice to make and a brave one. It takes hard work and dedication whether you're 20 or 75. You must accept the choices that you have made and the life you are living. You can change your economic, social, and educational status for the better. But you will always be a mother and hopefully always be a wife and those two things must take priority over the fleeting good times you might get at the clubs or going out with friends.
I know you can do this--just the fact that you wrote about your issue means that you're mature enough to handle whatever comes your way. Just remember you're not alone. You have to reach out to others if you're feeling overwhelmed. Any mom who is asking questions is a good mom!!
Take care and good luck!!