I'm sorry that nobody replied to your post. But I'll try and add my two cents to see if it comforts you in anyway.
I don't think that anxiety causes speech issues - per se (however I am no medical expert) but what I do know is that anxiety causes you to overthink and worry about everything, and when your brain isn't 100% focusing on a task and you have other things going on in the back of your mind it will cause you to falter in your speech. Example: If I'm trying to speak, even if just to someone I'm close with me and I'm worried or panicked I will constantly fumble over my words or pause in-between what I'm saying or just even "zone out", sometimes I will even forget what I'm trying to say. The shakiness that you describe is also something I've experienced.
If you're so worried about anxiety/panic it makes it hard to focus on something else - so naturally it will be more of a challenge to speak "correctly" and even write "correctly" if you understand what I mean?
I truly don't believe you have a brain tumour, actually I'm 100% sure that you don't. Try to completely relax before you start signing or focus on your speaking/writing when you're in a calmer state and see how much of a difference there is!