I worked out for years ... years! ... and could never compete with some other guys. I just wasn't capable of putting on the mass and strength. Genetics can be limiting and it's nothing to be ashamed of. Are you getting stronger and feeling better? If so, then don't compare yourself to others. If not ... then maybe you need to look at your program. Some people recover faster than others and you might not be recovering properly before pushing it again.
Also, muscle types play a big issue. People with what is called "fast twitch" muscle structures tend to have explosive strength but fizzle out quickly. People with "slow twitch" muscle structures have higher endurance but can't move as much weight. If you have a "slow twitch" structure (which it sounds like you might) coupled with pulmonary issues, moving big weights is going to be a battle for you. It's all personal and the only thing you need to worry about is you.
Second, don't compare yourself to women either. I was coaching my wife for the state powerlifting championships one year and she was bench pressing around 225 lbs. She could out-life plenty of men in the gym. Why? Because of the way I was training her, the diet I had her on, monitoring how each lift went, etc. But she's got some amazing genetics. What I'm saying again is that it's all personal. Just because they're women doesn't mean they can't move some metal and you shouldn't be comparing yourself to ... anyone.
Hang in there. Get healthy. Do the best you can and to hell with what other people are doing.