K.G.
Both my sons did similar things at that age, too, and they both went to day care. Here is what I learned that helped me:
My boys were doing fine at day care, but they did not feel fully comfortable and relaxed letting all their emotions out. Every day, even though they did great without crying, when I picked them up they would run to me and start crying on the way. They knew I was coming, but they were so relieved that they couldn't help themselves.
When we got home, they would cry and cling because they were so happy to be home and with us. They would wake up in the middle of the night and come into our rooms (they were in toddler beds) so they could lie down with us. They just wanted to be near us. Cute, yes. Annoying, yes.
This is also the age that nightmares start, or at least get more concrete. They did for our little men.
There were two things that helped us through this phase. 1: Patience. Your little one is learning more about schedule, routine, and the like, but he really just wants to be with you and is most comfortable letting out his emotions when he's at home. He bottles them up (or doesn't fully let them out) all day, so when he's with you, it's time to get them out! This stage does not last forever. 2: Time together. As much as you can, spend time with him just "being." Go to the playground and play with him. Push him on the swing. Sit down and watch football together. (My oldest loves football and will pull us in the room with him so we can explain it to him. He still doesn't understand it, but great memories!) Read books. Play catch (or teach him). Cook. Something where you can be together, close, and all your attention is on him. It is exhausting, but it really helps to get through this phase.
Good luck!