I studied mathematics and I was taught to draw pictures if problem is too hard to solve. What kind of tools/programming languages there are aimed to draw pictures for math problems? Should one learn Tikz or some programming language?
The range of software in this category is quite vast. You will need to do some research to find items that satisfy your precise needs.
I have used https://www.desmos.com/ to make drawings in two-space. You can use https://alternativeto.net/software/desmos/ to investigate related possibilities. And this site may help you to find something like Tikz.
I think it's reasonable to say that, most open source mathematics systems have some form of graphics system for displaying various mathematical entities. Look for pages like https://en.wikipedia.org/wiki/List_of_open-source_software_for_mathematics for possibilities.
To answer your question directly, yes, you could learn Tikz. Alternatively, you could learn Python or Ruby. I am familiar with the former language and know that many products are available for it for manipulating mathematical objects. It's not difficult to learn the rudiments of it.