Clingy vs. Dependence.

I don't like to be a clingy girlfriend. But from my previous experiences, both of my exes had told me at one point or another that I am clingy. Quoted from one,  " Jenny, you are an independent girl, but emotionally you are very dependent and clingy. " 

Is that possible?

I don't want to be known as a clingy girlfriend. I don't want to be known as a girl who depends on their man - I don't think I do, Do I ? I know that deep down, I have a lot of insecurities. Towards him as well as myself. But I've got to let those negativities go if I want this to work.

I just want to find happiness, I just want to feel safe and secure. I just want to feel love.