I have googled it. Google buzzing headlight.
I think you have a problem with the headlamp levelling motor. Inside the light is a small electric motor that controls the level of the lights from the dashboard somewhere. Its like a bolt with a little ball on the end. The notor yrns the bolt in or out to selct the lights aim. If the ball becomes detached it will hunt back and fore trying to find the correct position, OIn a few, but not many cars it can be replaced if faulty. The problem can be either ball come out of socket or a broken lamp. Because the headlight would have to be removed to repair it, and it might not stay repaired, it most likely will be chaper to buy another headlight if this is the case. I recently had to change my daughters light on her Panda. I bought a proper top quality light to replace it and it was a bit fiddlydoing the job so budget is 2 hours labour minimum. Our light was from shop4parts.co.uk and was £135 net of the discount for being a pid up member of the Forum. The lights can be had second hand but like all Fiat plastic things they are fragile. Other lights were available new from about £55 on ebay but you must be sure you are getting one thats suitable for a right hand drive car. I dismembered the old headlight to get the motor out, and on the Panda at least repair would not be an option.
Unfortunately its MOT critical so must be sorted before yur next MOT. Its just possible that it could be repaired but the time element will be the same. If you can find a genuine Fiat light second hand that would be the best way to go costwise. Whatever you do DONT buy a new light direct from Fiat as they will ensure you need a second mortgage!!
This diagnosis would fit the affected light having dropped low. Its not likely to make things worse by continuing to use it.
