Generally speaking, yes. Without special education (or rather, without a diploma of education) to become a programmer, of course, is possible.
However, if you do not need to study at a university, this does not mean that you do not need to study at all.
Yes you do.
And even if you have already graduated from a specialized university - this also does not mean that your training is complete.
Everything is just beginning.
As for self-education, when you have no special education in programming, then you have to learn even more - because no one will chew you up the material at the lectures and punish you for truancy, there will not hang over you the "sword of Damocles" of a threat to fail the exam.
That is, no additional motivation, except your desire, you will not have.
In addition, you'll have to choose your own study materials - and this is also quite difficult if you're starting from scratch.
So you could say that you're luckier than others. Because you have me )))
And my book "Fundamentals of Programming" which will give you a basic understanding of programming in principle and basic knowledge.