I have never heard anyone say 'I'm out of the words'. It doesn't make a lot of sense. A possibility is 'I'm out of words', meaning I have run out of words and can't find anything more to say, but this is not a standard phrase.
Just a thought:
I wonder if you have misheard the expression 'I'm out of the woods' or 'I'm out of the wood'. This means out of trouble or danger, or having got through a difficult phase. We often use this in the expression 'We're not out of the woods yet', meaning that there are still some problems that we might encounter on our way.
NB I believe there is a Taylor Swift song entitled 'Out of the Woods'.