Please don't let this turn you off on the program. This sort of thing does happen and it happens to those of us in AA too.
Sometimes there is a communication error and expectations aren't set out.
You don't have to rush to get another sponsor. Personally I think people rush into this too quickly. Go to meetings and feel people out. Think of it as an interview process in a way. You want a sponsor, not a "friend". Someone who will be honest and direct with you, not tell you what you want to hear. Sometimes it ends up being the person you would least expect.
When choosing someone sit down with them and discuss what the both of you expect and what you don't expect. Lay everything out on the table so that there are no surprises later on. Every sponsor is different and there are things a sponsor can do and things they can't. This is the time to discuss what you are comfortable with doing and what you are not. And you can get clear direction from them on what they expect from you.
There is someone out there for you, you just have to find the right one that is all. Sometimes it takes a little time.
Edited to add: big hugs to you, being rejected is not easy, I know. Hang in there and try not to take it personally, I know that it is easy to say.