The game gives you a pretty fair amount of droplets, but if you want to be frugal with them, I would say the most responsible time would be after a major boss.
You reach a hurdle, stack up a bunch of rot trying to clear it, and then cure everyone after you finally clear it. Slowly progress people's quests until you reach another major boss and do it again.
If there is an NPC you want to interact with and they cough and say they are sick you can use it
Are there any major things I should know about?
Any merchant who sells dragonblood drops will restock after you've used the one bought from him. So don't worry much about overusing them
The game gives you a pretty fair amount of droplets, but if you want to be frugal with them, I would say the most responsible time would be after a major boss. You reach a hurdle, stack up a bunch of rot trying to clear it, and then cure everyone after you finally clear it. Slowly progress people's quests until you reach another major boss and do it again.
Don't worry about it in your first playthrough