There are a few here who know a lot about SSA and SSDI/SSI. If none of them notice your post here then try the insurance/finances forum. The first thing you should do is bring this up with your doc and the old therapist maybe. You need them. SSA will send you for an independent evaluation with a psychologist but I don't think that evaluation carries much weight with the people who will make the decision on whether you are disabled or not. I know mine didn't. So having your medical team behind you is crucial.
And yes you should get the ball rolling as soon as possible because it can be a long process.
I do understand how you feel about it though. When I first applied my anxiety level was at 11 and the only room left in my mind was taken up by depression. Also at my core I am a very private person. The thought of opening up my life to the scrutiny of strangers whose job it was to judge me... it terrified me. I'll try to check back to see if the members who helped me understand the process post some answers. Good luck.