I feel the same way. My T is about 20 years older than me so that might have something to do with it, but also I think it's normal to feel like a child in therapy as it is the place where a lot of our feelings from childhood can be expressed. We're also being extremely vulnerable and basically begging for help, so I guess that's normal. Nothing to be ashamed of
For the writing, I'm sorry your T doesn't encourage it. Writing has given me the opportunity to bring up events I would never have been able to talk about. I don't understand why your T doesn't let you do things the way you want/feel comfortable to. As my T always says, if I can say things out loud of course it's better, but writing is still communication and it's better than never ending silence...
Take care