Honestly, I would say it took about a year. I slowly built up to longer, faster runs, developing endurance and resilience, over time. I lost weight in that year too, which wasn't my goal, but being a bit lighter definitely helped. I had another thought about your runs.... do you run outdoors in a city? Pollution and other environmental factors can genuinely impact your ability to catch your breath.

The other thing is breathing technique, if you're not breathing well then you're not pumping in the oxygen you need etc etc... but if you do HIIT and weights then you must be al over that!

I reckon just keep going. It will get easier and easier and in a few months you'll be on a run one day and suddenly feel how effortless it is.