I had an issue when I was an undergraduate mathematics major. Some of the professors felt that as an undergraduate, I could not do meaningful research; however, that was not the case. I did not let their opinions get me down and I eventually found an advisor that was willing to help me find a project and advise me on that project.
Please feel free to take a look at my blog to see the different projects I worked on as an undergraduate (in my portfolio section of the webpage) as well as difference topics that I am studying and interested in studying further now. I try to make my blog accessible to people with little knowledge of the topic (I know this is sometimes difficult to do), so I believe you might find it useful in finding new areas you could think about.
To view it, visit http://www.tylerclark12.com/blog.
Two particular blog entries that may be of interest to you regarding graduate school can be accessed at,
Most importantly, do not let anyone deter you. If you are up for conducting original research, then do it. It may not be as profound as other researchers have come up with, but it is a start and it is a stepping stone to the remainder of your career. I am very adamant that undergraduates should conduct research to see what higher level mathematical thinking is actually like - to give them the opportunity to see what they can do with their skills.
Do not hesitate to contact me if I can be of further assistance to you.