Iphone Calendar woes
You said you got a replacement because the screen was broken - can I assume that Apple replaced it? If so, did you ask them about the calendar?

In any case, I would try the following:


Perform a full backup.
Perform an iPhone factory reset
Test your calendars and see if it's still slow. If it is, then it's a problem with the phone. If not, then try restoring from your back and see if the problem persists.