If you think you’re becoming clingy, then its like that you are becoming clingy. I think the only way to do is to start finding some interests outside of your relationship to keep yourself occupied.
People are inclined to have rough times and then respond to them by wanting and needing more time with the people they love. And I’m sure your boyfriend understands that as well. At the same time, you have to get yourself together at some point and realize that nobody likes a cling-on. We all like some space.
So the best way to stop is just to do it. IF you notice it then you can stop it. Give him some personal space. Go into another room to watch television. Or start hobbies. It’s okay to be clingy sometimes. Just not all the time.