Is this sentence used correctly within the quotes?

I'm born and raised in the USA but I'm not the greatest with grammar. The other day I wrote a sentence in a way that normally I don't deal with involving 2 time periods within the same sentence and just wondered if my grammar was right? Of course I think it is but just want some clarification and explanation why or why not. I appreciate it !!
Here is the sentence in quotes ....
"I'm writing this email while you sleep in case I forget to tell you by the time you read this that I spoke to Rebecca last night."

I think it sounds right but to be honest I probably drafted this sentence 5 times till I thought it was correct so obviously my grammar is lacking. If I recall I had trouble deciding if the "forget" should be "forgot" but I decided to write it as I would speak it so that helped me decide.

Thank you,
Doug