Yes, there must be an association, it's little bit indirect, as alcohol can cause dehydration and dehydration can cause lower back pain by causing the discs to shift which can cause a compression of lumbar nerves or sciatic nerve (sacral nerves).
What you are experiencing is called Sciatica, check it out:
It seems as of recent study there are no best medication for it:
Chances are you can prevent it, if you hydrate prior, during and after drinking alcohol.
There are many factors that contribute to having your body manage the water differently, also each and everyone can be different. Some of the factors are the food you eat and the amount of Sodium in the food. I found this reference which describes the relation / association between dehydration (could be from drinking alcohol) and lower back pain.