Hi,
I'll hold up my promise and you'll hold up yours, ok?!
I haven't heard this with regard to a promise.
What I have heard is I'll hold up my end . . . The idea here is that there is a mutual agreement or bargain of some kind, and that I will do my part, do what I have agreed to do . .
It's similar, but I just haven't heard it with the word 'promise'.
If uou search Google, you get almost no hits for 'hold up my promise' but a reasonable number for 'hold up my end'.
Best wishes, Clive