Was there an [ellipsis](http://en.wikipedia.org/wiki/Ellipsis) after the `会いたくて`, as in `会いたくて…`? If so, then I think it could have the meaning of `会いたくて会えない`, but I think `会いたくて。` by itself wouldn't have that meaning, and would be an incomplete sentence which means "(I) want to meet and" (unless there's some context I'm missing here).

If there was a "but" before it, e.g. `でも、会いたくて。` etc on the other hand I think it wouldn't need an ellipsis after it.

I often see this usage of `〜くて` with some kind of strengthener before/after it, e.g. `本当に会いたくて…`/`めっちゃ会いたくて…`/`会いたくて仕方がない` and can also be doubled for extra effect in songs etc, e.g. `会いたくて、会いたくて…` (maybe you can do without the ellipsis in some of those sentences, I'm not sure...)