Your sentence is almost perfect, but it can be slightly polished for better flow and naturalness:
"I set a goal to read for 10 hours a month, but unfortunately, it seems I won’t achieve it. So, I need to catch up on my reading."
Changes made:
1. "Read for 10 hours a month" - Adding "for" makes it more natural.
2. Comma after 'unfortunately' - Adds clarity.
3. "Catch up on my reading" - "On" is the correct preposition here.
It sounds great now! 😊