Is it possible for toothpaste to cause teeth sensitivity?

I’ve been experiencing pain in a few of my top front teeth the last 3-4 days. They don’t look at different and the pain is most akin to when I’ve had cold sensitivity in the past, except that this is not limited to cold. The pain seems to happen based on touch in general.

I realised I changed toothpaste about a week or so ago to one I haven’t tried (macleans xtream clean lasting fresh if that’s relevant) and I’m wondering if that’s played a role?

Thanks in advance.