"Sorry to jump in," would be used if you need to interrupt a conversation. It would be considered strange behaviour to interrupt somebody else's conversation just to introduce yourself. It would be much more normal to wait for a suitable pause in a conversation between two other people, then make eye contact with them and then introduce yourself. When you are writing about yourself, I much prefer a style that involves writing "in the first person" = meaning "I am." But this is a style preference (in other words this is just my opinion). There are many people - perhaps even a majority of people, that have websites on which they sell their services but where they refer to themselves in the "third person" - e.g "John Smith is an experienced graphic designer." Some people think it sounds more professional to refer to themselves in the third person. Personally, I think it sounds stupid. So it is your choice..... (either is okay in terms of being correct English)

Be simple and direct. Dear Mr Smith: I am writing to introduce my ... Allow me to introduce myself as (a graduate student of XXX field) Check out the link below which contains very good sample letters of introduction. http://wenku.baidu.com/view/3e3cf226aaea998fcc220ee1.html?re=view