You can be any age to self publish. But, self-publishing means: being a publisher. It means marketing, distribution, editing, layout, printing (or managing contracts with others to print), and paying for all of the things a publisher does.
The only thing a younger age really does to the situation is that your legal guardian will have to be involved with any contracts you sign.
Self-Publishing is hard. It's an entire business model and therefore an entire job. Some people can do this, some people can't. It will depend on how robust your executive functioning skills are as to whether you have a chance of managing it. That's difficult at any age, and perhaps harder when you take on the burdens of feeding and housing yourself and others.
You're at an age where you can at least afford to make a mistake, and it probably wouldn't hurt you to understand the publishing industry if you want to write. I recommend you actually study the publishing world from both sides at some point and make the determination for yourself as to how you want to spend your time/money.
From a high level you'll be choosing between spending more of your time writing (traditional publishing) and a lot of your time running a business with multiple arms (self-publishing). Self-publishing doesn't remove the gate-keepers, it just changes who they are and how many people with experience are working to get your books through the gate into the domain of public awareness.