would " my heart is full of excitement, that it can't wait to watch the new movie that came out" be a dangling modifier?

It's not a dangling modifier, but there is an omitted word in the main clause that is needed to correctly tie in with the use of a "that" clause. This would read better, but it's still rather wordy and awkward:

My heart is so full of excitement that it can't wait to watch the new movie that came out.