Tree has been debate on other threads this week about how long to cut down or abstain from drinking prior to the DVLA medical, and it can vary depending on the person, how much and how long they have been drinking for. You only indicate having "a drink" on 3 occasions since Christmas, but that is not very specific....... Some people seem to have been OK with the medical after only a few weeks, while 12 is suggested as being fine for all but alcoholics.
if you put your application in next week, it could be several weeks before you hear about the doctor you have to see, and you have a 6 week window to have the medical so if you stay off the wagon you should be OK by the time you see the doctor if you go later in the 'window'.
if you completed a DDRS course you would have been given a list of insurance companies that look favourably on people who have been caught drink driving and done the course. If you didn't do the course, try he comparison websites, but be aware that insurance companies often quote good rates to appear to be best value, but then bump up the cost when you actually go to their site and complete full details.
the insurance company will want to know your reading in breath / blood, the length of your ban (after a course, not what you were originally given) and the offence code. The code is DR10 for drink driving, DR30 for failing to supply. There are also other codes but these 2 are the usual ones.