Dear Alexia,
First of all you should make us of longitudinal data functionality (in Project Setup):
Then you need to assign your "Baseline" questionnaire (called "Emergency Contacts" in this example) to the desired events:
Then, to modify the content of your Baseline questionnaire based on the assigned event, you can use Branching Logic (i.e., make specific field appear/disappear based on event names).
Here is an example:
As such, the field "em_contact2" will only appear in the event called "Baseline" (unique name "baseline_arm_1").
To find the events "unique names", go to 
and look for this column:
Best,
C.