The problem with threads like this op is that only the fit and healthy will answer. Leaving you feeling like a slug. The people who walk no further than their car door will not answer this thread. You are already doing better than most people by running 3km so hold onto that. and what other people do isn’t really relevant either. Because, well, they’re other people.
Lots of people who've answered are people who clearly state that they went from not being able to run at all, to developing that ability by slowly but surely training it. With lots of recommendations for apps like C25K, which is actually immensely helpful as it gives hope, inspiration and practical advice.
FWIW, I'm coming towards the end of C25K myself and am currently in the position of being amazed at how I've gone from seriously struggling through WK1, where you run for a total of 8 minutes in 1 minute increments, with 1.5 minute walks. I was genuinely in bits doing just that much, and I was a mad sweaty mess after it. I was doing it on a treadmill right by open patio doors and had to get a fan to aim at myself as I was getting so hot. (And this was not on especially hot days.) And I had the speed set to just 6km/p/h, which is barely a brisk walk.
It's honestly mind-blowing that I'm now running 27 minutes at 8.5/km/p/h, with the last two of minutes at 10km/p/h, because I could never run. Even when I've been at athletic levels of physical fitness in non-impact cardio and strength, I could not run for more than a minute without turning into a panting tomato. So now I know that even though just doing that last bit at a faster speed kills me and I can't quite see how I'm going to manage a whole 30 minutes at the faster speed, I know that in a month or two, if I keep running, I'll probably be smashing that too. And a treadmill is handy if you have one, because while it's definitely a bit different to running outside, I feel less embarrassed on a treadmill, both at home and in the gym, than I do outside where every random person can see me be completely crap. (I'm actually the same in the pool, I'm a poor-moderate level swimmer and I find myself too embarrassed to swim in the proper lanes until I improve, even though I see people who don't swim as well as me in them all the time.)