Hi Judi, I want to make sure I understand correctly:
1) You have both an iPhone and an iPad, and you just got a new iPhone, but you have the same iPad, right?
2) You don't have a twitter account, so you are just following by using instant messages with both your iPhone and iPad, correct?
3) Everything was working for you to read Twitter messages on both devices until you swapped your phone?
4) You didn't change any settings that you are aware of?
5) Do you have mobile data on your iPad, or do you get internet for your iPad via your iPhone or wifi only?
My best guess without getting answers to that question is that you were using your previous phone to mirror the messages that were on your iPhone to your iPad and when you swapped phones, that connection to your phone and iPad broke since it was a new phone.
I believe the steps you need to follow are on this page, under the section "Turn your phone number on or off for your iPad or iPod touch":
If this works for you, awesome! In that case I would greatly appreciate a positive rating. If not, please reply with the answers to the questions I posted above and I'll gladly work to help you get this fixed!