Depending on what you've written and what data structures it uses, it's hard to say, but:
I read that interrupts can't sleep, does that mean I am guaranteed that my handlers (hooks and read handlers) will be executed one after the other, or do I need to use locks to prevent simultaneous access to the same resources from different functions?
While it's true that interrupts aren't allowed to sleep, you also have to consider than an interrupt interfacing with this datastructure can also simultaneously run on another CPU, or another interrupt might stack on top of your your current interrupt being acted on, taking it temporarily off the CPU. In either case, you need to handle the deadlocking case, and the case that two threads compete for writes/reads.
So yes, there's no reason to believe just based on what you've written that you don't need a synchronisation mechanism of some kind. Depending on your particular case, you might find synchronisation simpler if you disable further interrupts on that CPU (eg. in the case of percpu variables).
What the appropriate mechanism is will depend on what you're guarding access to and how lengthy and costly that is likely to be, although since you are executing an interrupt, you're somewhat limited in that you can only really choose non-blocking primitives.