Well, if you're applying to Peds, it seems like it wouldn't matter.
I'd probably reupload a new PS. If programs have printed it out, they'll now have two PS's. But, they're likely to notice this anyway if you don't fix it. This is different from a usual spelling mistake. if you had simply spelled physician incorrectly that's embarassing, but I might leave this alone. This makes it look like you're applying to peds and IM, and might make IM programs less likely to take you.
So, I'd think about it this way:
1. If the program hasn't printed the PS and you upload a new one, they will never know the difference. You win.
2. If the program has printed the PS, then they'll see two PS's. That MIGHT make them wonder what you changed, and search for it. HOWEVER, if you don't upload a new PS, they're probably going to notice this anyway, so I doubt you really hurt yourself. So, I'll call this a wash.
Win + Wash = Win in my book. But, no clear right answer here. And you'll want to be ready for the "So, I noticed the use of pediatrician in your PS. Are you applying to Peds programs also?". remember that not telling the truth in your interview can get you into big trouble in the future, potentially.