I'm happy to help you write a letter if that's the way you want to go. However, I'll be honest and say it doesn't seem like the best way to me. By making that choice, you will put yourself in a position of being forced to come up with the "right amount" of information rather than basing the information given on how people respond. Also, it seems like a letter would automatically tend to give the impression of a problem rather than just giving an explanation. Finally, it probably will make people less likely to talk to you about it than if the information were given in more of a conversation. Although people are likely to Google it anyway, you will give yourself an advantage by being the first and primary source of information. That's only really possible through dialogue.
In my opinion, the better choice would be to begin giving it to people gently (co-workers, parents, students) when a question is asked about your cough or absence. Often, the conversation stops with, "Well, I have a disease called cystic fibrosis." However, it then offers them the opportunity to ask questions and you the opportunity to answer them and give the information you think appropriate for that particular person or group. It ends up spreading, but with you as the primary source, and people will be more likely to come to you with their questions (as opposed to spreading rumors) if they know you freely shared the information.
If you prefer to write the letter or would like to talk about this more, feel free to PM me. I'll talk to you about it or help you write, either one.