In my opinion the first thing you need is a clear understanding of what your goal is. Why do you want to be a linux admin? What do you like about it? What makes you say, "I want to spend my life configuring linux systems"?
If answering these questions requires more than 1 minute of your time, you are probably on the wrong direction.
Whatever you decide to do this is my advise. First, use internet. There are amazing tutorials out there for anything you want to learn. Find something that you enjoy and that makes you feel good. Experiment and "taste", the more you explore the easier will be for you to understand what you want.
Keep your job or find another job to cover your expenses. This means you have to work hard because probably you will have to study at night. I've been there, it's tough but at the same time you'll feel alive, I promise.
Learn and practice! This is specially important in computer science. Build something then try to find a way to break it. Once you broke it, build it again!
Go to meetups for people in the same field you choose. You'll learn a lot. You'll be able to start networking but mostly, you'll be able to measure your preparation and this will tell you when is time to start searching for a job.
Searching for a job won't be easy with no academic preparation. Start from the bottom and don't think about salary. For you is much more important to get hired than a good salary. Remember, you need to get hired once to be in the game!
I hired a PHP developer with a similar story as yours few years ago. I took extra steps to understand his preparation but at the end I couldn't ignore the effort and the commitment that this guy put into his preparation. Today he is a valuable component of my team and he makes me very proud of what he has accomplished.
Hope this will help!
[1] For instance: https://fedoraproject.org/wiki/Infrastructure
Give yourself an online profile with screencasts of what you can do.
Then sell yourself internationally as a trainer. Not high level stuff, but stuff you're very solid in in English language. Sell yourself not to large companies, but vendors of large companies. Charge fairly. Collect lots of name cards and keep in contact with people, especially the trainees (that actually work for the larger companies, but also keep in contact with the vendors). In a few years time you could be able to secure a very senior position with a larger company, or have already made a good enough living as a travelling consultant not to care.
But get those videos up and find a hungry vendor, that's step #1.
2) Install Gentoo
3) Set up ssh / webserver / mail server / irc / etc...
4) Buy domain and point to your server
5) Successfully run your own site/blog/wiki for a while, have it do neat stuff, write about and share your experiences of learning to be a sysadmin
6) While under oath, swear by the SysAdmins creed.
7) ???
8) Profit.
It's time to power network. Start attending local/regional linux meetups. Introduce yourself to the fellow attendees, try to be helpful, make friends.
Incidentally, this is where you'll hear about 'hidden' job opportunities. Say a contact realizes you know your stuff. He thinks you look normal-- he'll be more likely to refer you a hiring executive in his network who could use someone with your skills/background.
Check out Linux meet-ups--find one, get it on your calendar & go asap> http://linux-user-group.meetup.com/
As they say, once you know the why, you can figure out the how.
First, stop using the word hobby! If it's an hobby it's an hobby, if it's a profession you have to be professional!
Second, the way you are describing your experience doesn't really help you. It's too vague. Describe instead the problems you have faced. How did you solve them? What kind of value were you able to add to the entire system? (more stable, faster,...)
Hiring someone is an investment and a commitment. To pass the investment part you have to prove your skills, your ability to solve problems, your personal motivation and your growth potentiality.
The commitment part is more subtle and complicated. It mostly applies to the employer and it would take this conversation too far away. To keep it simple I can tell you that is very very important to get information about the company you are interviewing for. Try to think which challenges they may be facing and ask about these challenges during the interview. Think to possible solutions to these problems and discuss that with them. Don't worry about being right, nobody would expect you to know exactly the problem a company is facing but it would show vision and initiative on your side.
Last suggestion, you say "I know what I'm doing but...". No you don't, you would have a job already. Keep pushing. Do not fall in the stupid trap of thinking that the world is against you. I don't know you but I've been around the world many times. I can tell you that you can make it. Don't give up and keep working on your skills!
Good luck
There are tons of tutorials online that can get you started.
Once you get some experience, apply for a job.