No, this is not possible while video calling on your phone in the app. When you're video calling with your phone, you won't be able to access the rest of the app.
However, you can also make video calls from the NiceDay web environment! Log in via web.niceday.app to video call your therapist on your computer. During a video call on the computer, you can look at your registrations on your phone!
More information about video calling via the web environment can be found here.