IPhone has been broken for a week, will I get my texts from during this time?

The last my phone was backed up was on 4/12 but it's only been broken for about a week.
I just got a new phone and haven't gotten any messages yet, when will I if I do?

Added (1). I have the same SIM card if that matters

I would call the place where you got your phone and ask thern about it

Maybe. Usually the threshold is 2 weeks.

Was your "broken" phone attached to a charger and possibly on in some state? It's possible it could have received the text messages in some capacity. Otherwise if you are not getting any old ones it is what it is.