Potential advisor does not seem willing to accept me into group. How do I approach others in the same field? I have been trying to get into this professor's lab right from the time I joined my PhD program last Fall. We are in EE, and she does very theoretical work which is what I want to do. 

She told me in our very first meeting that she wasn't sure of my mathematical abilities to cope with her research. I took all her recommended classes, and this quarter I took a project-based course with her. I chose a theory-heavy topic hoping to get good results in it and impress her with it. 

However, I haven't got any results for the problem I chose. I have been working on the problem for a little more than a month, most of which time I took to just understand the existing literature. 

The professor's senior students consoled me saying it's a hard problem, but regardless of that, it looks like the professor is not going to take me in her group (she hinted at this in a meeting last week). 

So my question is: my university has lots of professors who work in this field, but only this one professor in my department who does this work. If I approach faculty in other departments, I am afraid that they'd just ask me to contact this particular professor, since she is known exactly for my area of interest, and is in my department. At that time, I'd feel very embarrassed to admit that I am going to them only because this professor rejected me. 

What can I do about this? I am sure people get rejected getting into labs all the time. How do you approach alternate professors? 

I also want to point out that though the professor doubted my abilities to do theory research, I do want to continue at least trying to work on my current project for a bit and do not wish to change my area of interest without even giving it a fair shot.
That is a tough situation. Any advice should depend on the specifics of your school. But I would advise to ask another professor to join their group, and when asked about going to the original professor simply say very briefly that she was not very interested in your idea (not in you personally, your idea) and so you wish to try with other professors. Don't give too much details.