I need to know before I book my son to get him checked....

My baba and I came to visit my mom who lives in a different city. This happened on Monday and he turned 3 months on Wednesday.

Since we arrived, he has been having a bit of trouble sleeping at night....he moves a lot! The first 3 nights he slept through the night but moving a shit load and then last night he woke up twice to eat (he would usually wake up once and sleep sooooo great) - so now, I know this is all new for him and he is more alert and exploring more and wanting to see the world etc....but is it normal that he moves soo much at night? He is not uncomfortable (he might be a bit warm since it’s very hot here but we have a fan), and he just only seems to settle when I put him on my chest then he falls asleep then wakes up moving again and blah blah. Is this sleep pattern normal?