Jitters/trembling

My baby boy just turned a month old yesterday and about a week and a half ago his bottom lip and legs started trembling like he’s freezing but he’s not and it happens at random times. He doesn’t cry or show any sign that it hurts but after reading something’s I’m concerned it maybe something serious. I was going to wait until our next appointment but my friend (who has two kids herself) made mention of him being “cold” and I said no sometimes he just does that and her next words of “aww your just gonna do weird things like Gretchen arent ya” are what made me realize it’s not normal.

Does anyone else’s little do this and if so have you talked to a DR?

Thanks in advance!