Should I be able to feel babies head?

Was using the bathroom and felt a strong contraction. Felt down there and there was something squishy right at the vaginal entrance. Then, pushing a single finger inside, I felt a slippery sac and a harder surface. I think it was babies head.

Should I be heading to the hospital? I am 38+1... and we're expecting to have a bad snow storm so I'm trying to take that into consideration before I am snowed in, in labor.

What should I do?

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