I have to write a 100 word summary of my research interests for a course I am going on. I'm not sure how to write it. Am I allowed to refer to myself in it? e.g. use I and my etc.

I suppose it depends a bit on what kind of course you are writing this for. If it is the basis for selection onto say a topic-specific summer school, I would definitely use "I". They want to see if your interests fit the course, so explain what your interests are! If you are already advanced in your work you can also be more "neutral" and show what you have already done, some results, rather than what you are interested in exploring in the future. It's really up to you. I'd try to figure out what the summary is for, that is, what whoever reads it wants to get from it, and then supply that.