I strongly suggest you applying for both master and PHD.Nowadays, it's really hard for undergraduates to get admitted by PHD program. However, you may try some not so famous schools.Good luck!
The most important thing is that you are not mature enough. I mean, in research. Once you apply for PhD and even you are a genius, you may find yourself not so interested in the area you chose. I suggest you start from a master degree. You are quite outstanding, all you need is experience. Good Luck!