Got yelled at today by old lady

So I was at the gym walking on the treadmill with my headphones on. Well I hear someone continuously coughing (very loudly) I can hear it with my headphones on, I see it's an old lady on her bike. When she's done coughing, she hacks up luggies into a towel and puts the towel in front of her on the part of the bike with the display and such. Kinda gross but whatever.  No big deal. Well I was done with my workout and got my 3 and 5 year old out of the childcare, getting ready to walk to the car. Of course my kids are not behaving and my 3 year old runs to the door and starts pushing the handicap buttons while the 5 year old is trying to get a cup of water. I see the 3 year old is getting ready to walk out side by himself so I grab my 5 year olds hand and drag him with my outside so the other child doesn't get hit by a car. My 5 year old starts crying the minute I grab his hang because he was about to get some water but I didn't let him because I was more concerned about the safety of my 3 year old. We get to my 3 year old and as I'm about to lecture him about not running away from me etc. the same coughing old lady proceeds to tell me my son pushed the handicap button and she got hit with the door. I apologize and tell her (as if she couldn't see already) that I have my hands full with two young kids and I'm pregnant. She says "yeah well I'm handicapped." So I get really frustrated at her. At this point I had one kid in each hand while carrying my purse and both their backpacks. Both kids crying. So I get frustrated and tell her "you probably shouldn't even be at the gym anyway with that cough you have." And I walk away. I know my kids were acting up but...it happens. Kids can't be perfect 100% of the time and why was standing in front of the exit door in the first place? Just frustrating... I'm literally just trying to do my best and feel like I'm drowning most days...😫