Your Choice
The thing you need to know is that you chose whether to participate or not. If you don't want to keep a journal, or have a conversation between different parts of yourself, that's your decision.
It's probably worth thinking about why you don't want to do something. Often it's because something feels unfamiliar. Maybe you worry that you won't do it well enough. From a counselling point of view unfamiliar can be great. It means you don't have a whole lot of habits associated with the activity. So you may find you discover things when you draw, that you're skilled at not noticing when you talk or write.
You're not trying to paint the Mona Lisa, you're looking to uncover and change patterns that no longer serve you well. Doing something different is often a good place to start.
Respect for you
However different their approaches there are some things most counsellors will have in common. Their main concern will be you and your well being. They aren't interested in judging you, that only makes their job harder. They want to understand what's important to you because that helped them to work with you more effectively.
They won't go home and gossip about you. What you say stays confidential. The only exceptions are a serious risk to someone's safety and talking to their supervisor. The supervisor is an experienced counsellor. Their focus is on your counsellor's work with you, making sure it is effective, ethical and safe.
Counsellor's are usually pretty comfortable about people expressing their feelings. They've done their share of crying and yelling and laughing and sulking. They won't be embarrassed by the emotions you express or talk about. Your feelings are part of you, and they will be welcome in the counselling room along with everything else you have to bring.
Your counsellor will be full of ways to support you to make the changes you want. Whether it's motivation to keep trying, appreciation of your effort and the progress you make, or ways to develop your ability to live the life you want, your counsellor can help you to make a difference.