My 3 year old been like this too, started pre school start of January and his separation anxiety got bit worst. However, he is settling really well in pre school, we just have crying when I am leaving. But at home he will not leave my side and makes it difficult to do jobs or go bathroom when you need to, but lots of reassurance, cuddles and patience as they little only once :) xx
My little girl is like this and she's 14 months if she sees me leave the room she will scream and none can calm her down until I get to her. It's driving me crazy. Because I get no break at all I'm literally with her every minute of the day until she goes to bed 😅