Can anxiety cause slurred speech? And if it can, can thinking about make it worse

Universal suspect. Anxiety is a prime suspect for almost all symptoms - especially the "soft" ones w/out known lab tests or imaging. And, certainly - thinking about it makes it worse. In fact, you have a great Dx Tool here! If the symptom can change based on distraction or focus - it's probably anxiety. Fractures, tumors, poisons, viruses, etc. do not come or go in response to a phone call, great song, annoying chat.
Yes. Some people are known to stutter or develop tics when anxious. People with stage fright are often worse - they are unable to get any sound out at all. The mind is a funny thing... it creates all sorts of havoc for no reason; but also, it adapts. People with speech impediments can train to overcome them. See _The King's Speech_ (movie) - a very good depiction of treating the problem. Best of luck!
Yes. Unfortunately the more you think about things. The worse the anxiety can get. Talk to your doctor they have several different treatment options. Some medications other behavioral options as well. .
Anxiety. Hi, Anxiety can cause a battery of symptoms, especially if you have panic attacks, thinking about the worry though could cause a vicious cycle, you need to learn some relaxation techniques, do some Yoga and meditation, also need to see a Psychiatrist to evaluate you for medication need or therapy. Good luck.