I SOOOOOO feel your pain. My attached little one is now 14 months and it has only gotten a tiny bit better. She has been this way since birth!!!
I had to give up the gym, can't do church, babysitters are out, and even grams and gramps aren't welcomed in her eyes.
I am a SAHM and felt like everyone around me blammed me for her behavior. But I didn't hide her away or never go out of the house. We even did play dates and were out among people as much as we could. However she was and is just very shy and loves her mommy... there was even a month where daddy couldn't hold her.
It does get better, but like I said she is now 14 months and I can only kinda see a light at the end of the tunnel.
I just came to realize that this is who she is. We didn't do anything to make them this way, it is just apart of their make up. All we can do it keep on putting them into situations that make them get to that place of feeling those fears and showing them that it will be ok. I think my on going outings and exposure to other kids and adults has helped out. Some days she is braver than I ever thought she would be and others are same old same old :)
One thing I will say is that sometimes WE tend to be the issue. If they see us they tend to melt down a bit more. My little one has been over to my sisters house a few times so my hubby and I can go get a bite to eat. We sit down with her and get her used to the room and the new faces (even if it takes a 1/2 hour) and then we sneak out the door when she isn't looking. My sis tells me while there is a bit of looking around and heavy breathing (sometimes a few tears) she gets over it fast. BUT of course the second I walk back into the room the tears start flying and she runs to me.
So I would suggest finding someone you trust and just asking them to help you with this... Make sure she is happy and ok with the person, in that while you are in the room she goes up to them or is excited about the toys ect. and then make your move. You don't have to be gone long, but give her time to be apart from you. Yes she may melt down, but that is why you have to find the right person. A person that knows the issues and is willing to ride it out while you are gone. If they have kids even better, so she can get even more exposure to others.
Practice practice practice is what we do in this home :)
It isn't an overnight fix, but we keep at it daily and have great people in our life that are willing to deal with her and help us with it. It hasn't been easy and I know I have more work ahead of me, but she is worth it. And I have another one on the way in September so we just hope we don't get another overly attached baby! What fun that will be :)
Good luck...