does CRM solve my Problem?

I never used a CRM and I just watched some YouTube Videos about different CRM solutions. Still I'm not sure if my problem will be solved with a CRM Software. I hope you guys can answer me this question.

What we do:

We are dispatchers in a security company (I hope thats the correct english translation). We decide which of our personnel carries out which job. On one hand we have to consider law (working hours, rest time etc) on the other hand we have a lot of wishes from our personnel (want to work more / less hours, wants to work for a specific client etc).

The latter is hard to track. We have to remember who wants to work more for the next two weeks. Who wants to do a specific client not more than once a week. Someone wishes to work only at daytime for the next month. Who always helps out if needed? And so on…

So far it kinda works, but a software solution might help us. Would a CRM solve our problem? I am worried that a CRM doesnt have what we need or is too time consuming (we are often under time pressure)

Thanks for your time