fenix welcome to the forum! Yes, CFL bulbs and other fluorescent lights flicker too (and so do incandescent lights), but the pattern of their flicker is different from that of LEDs. And the flicker of LEDs varies widely in different lights. Extremely rarely, LEDs are engineered to not flicker at all, but unfortunately, manufacturers now often mislead the public by advertising flickering LEDs as flicker-free.
Before LEDs, incandescent and fluorescent flicker didn’t bother me, except perhaps mild headaches after a day working in fluorescent lights with some of that time on a screen. Now, flickering LEDs trigger severe concussion-like symptoms for me in seconds to minutes, fluorescent lights will start headaches within hours, and even incandescent flicker, which is the least irritating to me among flickering lights, will cause headaches or restart symptoms during months that I’m recovering from serious LED flicker exposures. Only non-flickering light, such as sunlight or completely flicker-free LEDs, doesn’t ever trigger symptoms for me now. It’s possible that if you aren’t too sensitive, you might be able to tolerate CFL or incandescent flicker - I still could for a while until after my most serious LED flicker exposure. There’s a discussion about finding actually flicker-free LEDs here: https://ledstrain.org/d/1176-flicker-free-led-lightning-its-the-most-important-thing-which-one-to-buy
I’m in the US and only buy flicker-free Centric Home A19 bulbs from Waveform Lighting.
Unfortunately, just buying a screen with flicker-free backlighting, assuming they’re telling the truth, isn’t enough to eliminate screen flicker because there are still other forms of screen flicker including temporal dithering - there’s many discussions of this all over this forum. I personally haven’t found any screens that don’t start my symptoms, including trying a “flicker-free” BenQ screen - it triggered symptoms faster for me than my old CCFL screen that has a little backlight flicker.
You might be interested in some resources I put together about light and screen flicker here, including drawings of different kinds of flicker and lots of links to references: https://www.flickersense.org/background/led-lights