@alana
Good for you using a pull up.
I can remember those 1st few times leaving the house in a pullup. I "knew for sure" everyone else "knew for sure". Yup, nope. I have been in pullups daily for a number of years. At this point its like putting on "regular" underwear for me.
I believe people are too busy and unobservant to know you are wearing a diaper. Think about it yourself. Prior to you needing something did you check out everyone's pants/skirts etc around you and wonder "are they wearing a diaper?" Bet you didn't. So by default I would wager heavily with you neither is anyone else. I remember having wet spots (sometimes areas) in my pants before I went to a pad and then finally to a pull up. Trust me that sticks out, big time! I'll take my chances on the occasional person who figures it out vs. the obvious wet pants every time.
I don't want to discourage or depress you but until you can get figured out why this is happening to you, you are probably going to have times where you consciously and knowingly wet yourself. It may seem like the end of the world but it is not (as long as you are wearing something absorbent). Mentally it seems "wrong" but I have been there many times where you just physically cannot hold it any longer and it starts to come out (thinking of the example with your son in the bathroom). Sometimes for me I cannot stop until I am done. Its a really weird feeling standing or sitting somewhere and wetting yourself but I know for myself I am not doing it for fun, I cannot help it. I remember in the beginning it was really hard to adjust to that. Now after so many years I just kinda go "yeah whatever thank goodness for good diapers", find a place to change if possible and move on with the day/evening.
This may be another question you re thinking: "yeah but wont everyone around me know I just wet myself?" Probably not especially it there are no leaks to see. I have been in cars with friends or family where I said I had to stop to use the bathroom but I knew I wouldn't make it. Once we found the bathroom I used it to change instead. Try not to panic or make a big deal out of it and bet you no one is the wiser. Some of that confidence is based on experience. Once you find a diaper you trust then having accidents isn't so earth moving as it is when it 1st starts happening to you. (suggestion: if possible keep spares somewhere with you. That way if you are stuck and have wet yourself at least you are able to change) I also keep wipes with me to "freshen up" a bit. And I when possible I use baby powder (cornstarch based) with a diaper change. Keeps odors down I think.