Angry Baby Kills Mom, Doctor

This is a question about a program I saw years and years ago on TV and don't know the name of.

Synopsis:
A new mom swears her baby's really ticked off at her for birthing it & her husband figures she's nuts. Before he leaves for work, he calls the Dr. & asks him to make a house call. Turns out the mom isn't nuts & the baby is running amok. I forget exactly what happens to the mom and dad, but along the way the baby slashes the Dr's ankles with his own scalpel (in an off-screen, safe-for-TV kind of way).

I'm pretty sure it was shot in black and white and what I remember of it has a 60s aesthetic.

I thought it was a Twilight Zone or Alfred Hitchcock Presents episode, but when I reviewed their episode synopses nothing seemed to match. There's a small chance it was a feature film, but I doubt it. (I'm not thinking of "It's Alive!" or "I Don't Want to Be Born")

Thanks in advance for your help (It's been bugging my brain for years!).