Been there. I focus during these perioRAB of anxiety on people I might have offended, and the anxiety doesn't go away until I have spoken to them.
there are other solutions to this problem besides medication, of course there are! Obviously alcohol is a terrible terrible thing to put in our bodies, fun, but ultimately destructive. So quitting would be the most effective solution. Goes without saying i suppose.. But besides that I've found that breathing exercises are very helpful in reducing anxiety - e.g. pranayama yoga, i recommend looking it up if you dont know it. Meditation is also good. Both of these exercises work to clear the mind of thoughts, basically tell that nagging swine to shut up. They take energy, however, and so aren't that useful when hungover, but if persisted in over time, anxiety will be generally reduced. For less severe feelings of imminent doom, be aware of the muscles of the face, jaw and neck. no doubt they'll be clenched. relax them, allow the jaw to hang open comfortably. This also regulates thought, as when we think, these muscles are being used, just as when we talk. For more on this, read Undoing Yourself with Energised Meditation by Chris Hyatt, and do the exercises in it - its available for free on scribd.com
Hope this helps - I highly recommend looking into these exercises and others like them.Medication is not a permanent solution. if it was, pharmaceutical companies wouldnt be so rich. I did pranayama for about half an hour daily over the course of a week and afterward had no desire to drink at all. a week after that i saw someone smoking and realised that i had given that up without even realising. Most importantly i felt really happy, really energetic, and completely free from any anxiety.