The email you keep not sending is rarely hard to write. It is hard to start. Most of the time it is waiting for a first line, and everything after that comes more easily.
This guide is practical help with the parts that stall: what the email is for, the first line, and what to do afterward if nobody replies. It is not medical advice.
Decide these three things first
3 things to do
Ticks are for this visit only. Nothing here is saved anywhere.
A first line to start from
The rest is usually easier once this exists. Use one, or write your own.
Pick the one you are facing
“Hello, I am hoping you can help me with something.”
“Hello, thank you for getting back to me. To answer your question:”
“Hello, thank you for asking me. I am not going to be able to do it this time.”
“Hello, I got in touch about this a little while ago and I have not heard back yet. Could you let me know where it stands?”
Before you send it
Read it once against these, then send it. Reading it a fourth time does not make it better.
4 things to do
Ticks are for this visit only. Nothing here is saved anywhere.
When nobody replies
Chasing by the same route that already went unanswered is usually the slower option. If you emailed, try a call, or the other way around. And ask for a date rather than an update. An update can be nothing. A date is something you can hold them to.
Then note when you will check back, so the waiting has an end. If the follow-up is by phone, scripts for the admin calls everyone dreads has an opening for chasing.