The first thing you should do is turn off all power to your house to prevent an electrical fire or a shock while you’re troubleshooting the issue.
Secondly, check to make sure the size and wattage on your light bulb is appropriate for the fixture. Usually the wattage rating for a fixture is printed on the insulator where it screws in.
Next, ensure that the light was installed appropriately. A loose light bulb is prone to overheating which may be causing the burns on your ceiling.
If the wattage is correct and it was installed correctly, there may be a complication with the wiring. If this is the case, contact an electrician to diagnose and repair the problem. Attempting electrical work without training can be extremely dangerous, so when in doubt, always call an expert.