Most Helpful Guy
Just talk to him and see what he is comfortable and come up with some code word that you both can say mutually if things get. Too "clingy" and you can then both know to switch to just holding hands and being less drunk on love.
Most Helpful Girl
Not everyone's definition of clingy is the same. It depends on what yours is, and his.
It's important to make it known that you want to keep in regular contact. Some people back off , and fear texting someone regularly , so they don't come across as too clingy. Instead they make it appear as though they aren't all that interest. The other person assumes they aren't thinking about them.
Text him now and then to ask how his day has been, and talk about yours. If he doesn't respond ASAP don't be overly concerned about it. Don't always be the one to text first.