Was there an 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" or "yeah" before it, e.g. でも、会いたくて。/うん、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...)