Front left dip blown (again within few minutes)

About a month ago, my front left dip light blew, simple fix, and after a few weeks, it blew again, and i changed it again. Today, (after a few more weeks) its blown again, same one, so i changed it. (since i bought a pack of 2 and used one from that pack) When it blew however after getting petrol, it blew, how i knew though was because all lights, (the dip on the right hand side, speedo illumination) went MUCH brighter, the wipers sped up quite a bit and the battery light came on, then after a while, about 10 or so seconds, it went back to normal and i noticed, one side of the road seemed a bit more dim, so I stopped for a bit to look, and it was the same dip bulb that had blown, so I got home and changed the bulb with the last one i had, then i had to go back into town to do a small amount of shopping, and as i left the shop, 10-20 mins after i arrived, i started the car up and it seemed ok, then i left the junction where the shop was and noticed the battery light on, wipers going fast again, and lights going brighter, so i pulled over in this small car park, where i had to look and see that it had blown again, minutes after i replaced it, and i continued to another shop, to get fish and chips, the entire journey, the battery light not going off this time, also the speedometer getting to 10mph, but then dropping to 0 suddenly, (also the fuel needle dropping to 0 the same time the speedometer needle drops) so i stopped, turned the car off and got my stuff from the fish and chip shop, started the car up and it, seemed ok (apart from the dip that blew earlier) but as i pulled off to go up a road to turn around and head back home, the battery light came on again, so i thought if i turn full beam on, put the fog light on and put all wipers on full would drain some of that charge, just to see if it would go off, it did for a while until i got up to speed, (speed limit, 30MPH) (by now i had put the full beam off and fog light off since i was in a town and there were more cars around) and it came on again, so i realised it didnt work and i put the wipers back to normal speed, and turn the fan back down, and continued back home, where the battery light was on for the entire journey. Im just wondering, as i think i know the signs but i just want to make sure, is it an alternator problem? Overcharging a bit too much? Or is it something else? Like a short circuit or something else?