Your text is something I could have written one year ago. While I was able to spin or swim extended periods of time, I was never able to run more than a short sprint without going beyond my limits. For some time I was quite sure that I simply COULD NOT run and would never learn to do so just like others couldn't swim.
While my husband was going for a run, I was running the distance between two street lamps and then walking for some minutes and repeat.

Because I felt stupid walking around in my running clothes, I started Nordic Walking. Nordic Walking gets the heart rate up a little higher than just walking AND made running slow and relaxed easier for me (I guess because there is less weight on the leg muscles). With the walking sticks I ran the short distances between 2 street lamps, then slowly upped the distance. I read quite a lot about correct form, tried to up my cadence (up the cadence while slowing down overall!) and correct my posture. It took me about half a year to run the whole distance (about 5 km, my husband was able to run this far from day 1).

After some time, I stopped using the Nordic Walking sticks and didn't need them anymore (I still use them sometimes for mountain runs). It has been one year since I started running and I am now able to run for about 10km.

I think some of us just need a little extra time because they aren't really talented runners. But it pays of, it will be a lot of fun in the end, don't give up!