"I wanted to explore what it feels like to write a parser, a lexer, and an interpreter without using a framework or some other ready-made solution"

This is an excellent exercise for any programmer who wants to really understand what's going on behind the scenes. I've always believed it's useful to understand at least one layer below what you normally work with.

Some people will criticise you for "why create another programming language when we already have X?" but ignore them. As long as you explain that it's an experiment (as you have) you should be fine. And it's possible that by starting something completely from the ground up you'll discover a different take on things that might be better than what exists already.

Just be prepared to do a complete rewrite or three once you've got your initial prototype working ;)

"and I didn't really consult any literature either"

I really recommend that you do.

The single best resource on this topic is the "Dragon Book" (officially "Compilers: Principles, Techniques, and Tools" by Aho, Lam, Sethi, and Ullman) - the latest edition is from 2006, though the older one should be fine for what you want too. I wrote my first compiler before learning the "proper" way of doing things and it was a complete mess. It was only after studying compiler construction at university that I learnt about things like formal grammars, syntax trees, etc. The dragon book will take you all the way through to expert level, and is written in such a way that you can implement different parts of your compiler as you go through the book.

One caveat though is it's huge (close to 1,000 pages). I spent a couple of months full time working through it (coding as I went along) during a long break from work a couple of years ago, and only got about half-way through in that time. But you only really need the first few chapters to get the basics; the later parts go on to a lot of advanced code optimisation techniques that you only really need if you're trying to write a high-performance production compiler or get into compiler research.

SICP, as someone else mentioned, is also very good, though it's really more about the overarching theoretical concepts and doesn't go into the same amount of depth as the dragon book. I think reading both is a good idea.

Just be warned, this stuff is highly addictive, and you can spend years studying it and still end up with lots of gaps in your knowledge ;)