How to deal with my insecurities about my race?

I am 1/4 Japanese and 3/4 Scotch-Irish, German, etc (not sure about all the percentages of those). I have always been strongly connected to my Japanese side and have always dreamt of going to Japan. However, I feel like only being 1/4 Japanese, I am undeserving of partaking in the culture and going to Japan. I absolutely adore Japanese culture, but I feel like I'm unworthy of it. That I somehow shame it. I know it sounds absolutely ridiculous, but I'm terrified and ashamed that I'm not full Japanese. It also doesn't help that my mother keeps telling me that when I go to Japan, I won't be accepted because I'm not full-blooded Japanese. How can I get over this feeling of inadequacy? Honestly, I get so worked up over it that I make myself sick. I know I can't change it, but I still wish I could. Does anyone else deal with the same problems? I'm not trying to be racist, these feelings are only pointed at myself. I just don't know how to deal with them. Can anyone help me?