Is it clingy?

So, I'm in a LDR. Luckily, he only lives a few hours away so it's possible to see each other at least once a month. We talk everyday over some format, usually g-chat or texting though occasionally we call. I've had a problem with being emotionally dependent and a little clingy in past relationships. After my last long-term relationship, I did not see anyone seriously for a while, hoping to work on this issue. My current boyfriend (we were casually flirting and eventually casually dating at the time) helped me through it a lot. However, I stopped seeing my now-boyfriend after some strained contacts and started seeing another guy who reminded me a bit of my ex. This started up my emotional dependency again I'm afraid.

I broke up with that guy so I wouldn't fall too hard into my old habits and now am dating my new boyfriend (he makes me feel much more confident and able to take on the world, so I was hoping it would be ok) but the difference between them is unnerving I guess. Where my recent ex would constantly text me, my new boyfriend only texts me a couple times. Only if he really has something to say or thinks of something funny and one of us isn't online or something like that. I got into such the habit of texting, it sometimes feels weird to have my phone be silent. (of course, if we're both online and not super busy, we talk a lot more. He just doesn't have unlimited texting.)

So, basically my question is: am I being clingy to want to text him a lot? I don't. I will usually just tell myself to remember it later and tell him online. I guess I've just been feeling extra bad about it because he had a friend in town so we talked significantly less and I wanted to text him more. I just don't want to mess this up. He and I have been through a lot together and I care about him. I'm pretty sure he cares a lot about me too. Thanks!