My agoraphobia is triggered by my social anxiety. I never realised that I had it until I had to go to court concerning an appeal for ESA benefit. The judge and the doctor sitting on the appeal kept on coming back to a sentence I had written on the form. I sit in front of the cupboard quite literally for hours unable to pick out what to wear. Adding to it is that I seem to have a dislike to showers as well. It takes me ages to get myself to have a shower (ages as in a couple of days). I won't leave the house at all looking less then perfect ( make up, proper clothes etc), and that is only when I can't avoid going out at all.
I have noticed that I am able to do things when it comes to my son. I have been to meetings with him, have made phone calls for him (extrem phone phobia means I only use my phone to talk to ca 3 people, son, mother and ex husband) etc. in the past.
For myself it seems like a tower... Low self-esteem at the bottom, pain (I have fibromyalgia), even more low self esteem, more pain, panic attacks, social anxiety and now worsening agoraphobia. Now if you add traumatising life events to this tower you have the leaning tower of Pisa

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I know, this might not be of much help to you. The one thing I do know of my anxiety and phobias is... As more I give into them as worse it gets. Getting help for it should be simple, and I know social anxiety is very treatable, but it takes ages. I have tried for nearly a year now, and have had counselling prior to this. But I am still waiting to see a therapist. (counselling is good, but as a pain psychologist agreed with me... It didn't go deep enough.)
Coming back to your post,... If Skype doesn't work for you (it wouldn't for me) find another therapist in the area you are going to. Look into your options of therapy as well. Usually cognitive therapy is used to change the way you think... Counselling can raise awareness... All of this can be very helpful, but it wouldn't work for me. Key is that you feel comfortable with your therapist. This will make it easier to attend sessions. Maybe you could phone a few therapists up to just get a feel for them before you decide seeing someone. Most therapists are happy to talk to you prior the initial assessment... Ask questions to their experience in the line of help you need etc.
As for appreciating the support of others like your parents but not wanting to rely on others... My son is exactly like that. He is 18, has social anxiety disorder and I would say he put me into the driving seat of his life for about two years. Then came the point which you are talking about... Independence! Wanting to be independent is the best motivator you can have. The way my son did it was to sit down with me and talk to me... Explaining that he feels ready for it, and also asking me to push him if he needs a push... (before I would have tried to protect him). Now, if he asks me to do something for him, I gently remind him of the independence bit and he realises that it would be a step back if I were to do things for him. I'm not sure if you can see a link here but my son and myself had a codependent relationship... Not good for neither. On the other hand, keep in mind ... How many twenty year olds have moved out and left home? In the UK not many. And how many of those who have moved take their washing home... Ask any mother

... A lot of them! What I'm trying to say is ... Don't be too hard on yourself.
Right, am getting the feeling that I have been going on again ...

... Sorry. The whole thing about agoraphobia just gets me going as it has played such a big part in my life. Let us know how you are getting on please.