I recently moved into a place with 15 steep steps and like you, it was hard to climb them and I actually had to stop halfway through for the first few weeks to catch my breath, and I actually tried to avoid going up the stairs as little as possible.
But then I just told myself you've gotta conquer this problem, and so I just started climbing them several times during the day and rested when I needed but kept at it.
After a month or so I don't really get out of breath on just one trip up, but tried going up and down several times in a row and I get really winded and even dizzy when trying to catch my breath.
And yesterday I tried carrying a heavy suitcase up the stairs and had to stop not even half way up to catch my breath, and when I got to the top it took several minutes to fully catch my breath and to quit breathing hard.