Awwww poor Misky.... I've been there (and still occasionally suffer from my back pain, especially when I've been over stretching or lying down in bed all due to a cold/flu etc).
If you find that the agony eases off during the day, it's almost definitely muscular and all you can do is take pain killers but KEEP MOVING. Obviously it will be agony getting up in the morning - try some gentle bending and stretching whilst still in bed (lying on your side), this may help you actually get out of bed. Then, when you are standing up, try touching your knees - ok, I know it will only be bending over an inch or so, but also do some sideways moving to increase your flexibility. Then you should be at least able to get into the shower.
Regarding the driving, if you can raise your driving seat, that might help, as will pushing the seat a little further back and using your ankles as pivots on the pedals instead of lifting your feet off the floor.