Hi, Neomi! You got some good answers,already...
"clingy" can also be a label given by someone who is afraid of intimacy, who remains aloof to avoid the pain that will want to free itself when love arises (just another perspective)
Dependency versus independence, that's a very ancient struggle: none of these attitudes breed healthy relationship.
From experience, I would say: don't try not to be clingy (if you recognize that you are), that won't help at all! Rather, it will turn into another manipulation to please the other, not to lose him or her.
I have suffered from aloofness and from "clinginess" both. Ultimately, they are both immature: we need two wings to fly, two legs to walk...
The way out of this gooey, dichotomous way to relate is not through repression. First, one needs to see oneself just the way one is (not how we would like or think we should be or not be). That requires ruthless compassion towards oneself, to be honest.
Actually, the way out is through the agony of neediness (which has nothing to do with anybody else) and own the responsibility for it. Aloofness is further away from the exit!
If you don't try to avoid the pain (hurts more!), you will see that it just wants to be released and leave you, forever!
and yes, it is absolutely true that clinging is a way to avoid our own emptiness; by avoiding it, we miss the peace, the silence and contentment of aloneness: whenever you are truly alone (not lonely!), your relating will be enriching, a true sharing;
welcome and "welgone"!
But first thing first: where are you now?
I wish you the best of luck on this journey, the most arduous one, I believe, except raising children! (although the same laws apply: most of us have children to avoid ...the void!)