With old drywall like yours, it's normal to have some cracks, especially if the ceiling has gone through temperature and humidity changes over time. In my apartment I had the same situation years ago - thin cracks that weren't moving anymore - and I found out they were simply due to the initial settling of the structure that was never fully resolved. The important thing is to understand whether you're seeing new cracks every month or if the ones you have have stayed the same. Check back in a few weeks: if they haven't widened and you don't see any new ones, the movement has probably stabilized.
What the others didn't emphasize well is that you should also check the opposite side - the ceiling of the room below yours. If the drywall there is in good condition and you don't see any moisture or sagging, it means the problem is really just superficial in your layer. Calling in a restorer for cracks of 2-3 millimeters is overkill and you'd waste money. You can fix them yourself with some drywall joint compound and a putty knife, which costs practically nothing. Apply a light coat of compound, let it dry, sand gently and repaint.
The only situation where you should call someone is if the cracks are widening quickly, if you see other cracks radiating from a single point (a sign of actual settling), or if you notice moisture stains around them. In that case, yes, there could be a more serious structural problem that requires a professional look. But from what you're describing, it sounds like normal settling.