While this may be the case, there is also the possibility that this isn’t really tied to alcohol withdrawal.
Alcohol makes it very easy to fall asleep and very hard to have high quality sleep. Others have mentioned this - but you may have developed an evening routine that (unbeknownst to you) relied upon alcohol to slow you down and get you to sleep.
Since it sounds like your problems are truly around falling asleep and not the total sleep time I would focus entirely on the evening routine suggestions others have posted here. I would not recommend pills at this point - you don’t have nearly enough data points (15 nights is not enough) to add what would likely become a permanent medication to your routine.
I’d suggest you look at the answers to the questions below, and probably others, and see if you can find the cause.
What are you doing in the thirty minutes before you fall asleep? Do you have a television in your bedroom? Are you exercising in the evenings? At what time do you stop caffeine consumption? How long before you sleep do you eat a large meal? A sugary snack?
It is also possible you are an insomniac or have another stress related sleep disorder that the alcohol was helping to mask. I would do everything I could on the above items before I considered medical treatment for something like this.