Yes, you should be concerned because you’re in danger of having water leak through your ceiling. The usual cause of this trouble is a build up of ice along the bottom edge of a roof. This is called an ice dam and it poses a roof leak hazard. Ice dams trap water that pools behind the ice, allowing it to leak between shingles. So far the problem exists close enough to the edge of your roof that the leaking remains away from your ceiling, but you still need to do something about it. Start by having enough of the ice dam removed to allow water drainage. That’s the short term fix. Preventing the problem will take more work.
The root of the issue is too much heat escaping from the roof of your house and melting rooftop snow when ambient temperatures are below freezing. This temperature difference causes freezing to occur and a berm of ice all around the edge of the roof.
Then temperatures finally warm above freezing, large enough amounts of rain and melt water will be stopped by the ice dam, forming standing pools and leakage further up your roof.
The long-term solution is to increase attic insulation levels while also boosting attic ventilation. Both these changes serve to lower the temperature of the outer roof surface, reducing or eliminating the formation of the ice dam. If it isn’t possible to make these changes, then permanently mounted rooftop heating cables are your only option. Turn them on when ice needs to be melted, then switch them off to save energy.