Hi to you from David 'The Famous Forry'
You can usually tell if your fridge is working as you can hear the compressor running , although the compressor switches on and off periodically as temperatures are reached.
This probably is just the bulb in your case but keep a close eye on precedings for the next day or 2. The bulb can be bought easily from your local appliance spares or online, like places such as ebay. Just type in fridge bulb or I can provide you with a link for a NEW BULB.