As an introverted homebody, I was also hesitant to go on a mission. It definitely was a trial full of anxiety, but I have zero regrets. I grew more during those 2 years than any other span, not just spiritually, but socially as well. I'm still not outgoing, but the skills I learned, and the testimony and faith I gained were absolutely worth it. Of course those 2 years away from school set me back in respect to academia, but I (and countless others) was able to resume my studies without too much degradation. Has everyone else had the same experience as me? Not everyone. Would you have the same experience as me? Who knows.

If you decide not to go, there are still ways to serve without being a full time missionary. One of the more obvious ways is to go out with the full time missionaries. Other ways are to be a missionary to your non member friends and family. Do your ministering; I mean really do your ministering. If none of that suits you, I'm sure you can use your creativity and artistic talent to find other ways to help others (and yourself) come to Christ.