>Honestly I'd say "get a knife" or a extendable baton, preferably an electric one
Cute, but no. Just get a pepperspray and be done with it. Aim for the eyes, shoot and run. Supereffective against stray dogs and scumbags alike. Is it manly? No, but it can't be used against you, having it in your posession won't cause provocation, it's cheap, easy to use, it spares you from soiling your hands and it'll leave you a clear and clean exit; it's basically the perfect weapon if your goal is to stay out of trouble.
I'd personally consider going to work in some kind of sports wear and jog on the way home, straight to the shower to cleanse yourself of sweat and the filth contracted from the dirty outside world.
On your agoraphobia: it will be tricky for a layman to give decent advice on this; general, nonsensical advice could very well do more harm than good. I will say, however, that phobias of this sort are usually best treated in group therapy, to my knowledge that is. Every case is subjective to some extent, a common trait is that cures doesn't exist - so you're left with training yourself to better deal with it. The purpose of group therapy is indeed to provide good, collective training in controlled environments. My point is that you might just be able to train yourself on your own. I'm with you in acknowledging that it's not easy. It's not easy, yet we have to somehow manage. You'll be okay - not because I say so, but because you believe so.