Hi Falling,
Firstly, you're not responsible for your exBF's alcoholism. He's the one tipping it down his own throat. So, when he blames you for where he's at right now, please don't buy into it as it's alcoholic quacking.
Also, don't beat yourself up for sleeping with him after breaking up. I'm sure many of us have done the post-break up sex thing..I know I have.
Thirdly, actions speak louder than words. He may still love you, but if his actions don't match his words then what are you left with? Confusion and uncertainty and he gets to keep you on a string...If he's still active in his alcoholism and he doesn't want to get help, then that's his choice. It's a hard pill to swallow that someone would choose a substance over a human being, but that's the nature of addiction. As for the future, I like many wish there was a crystal ball to see what's going to happen next, what's in store for the future. Unfortunately, we aren't privvy to that information. So, the next best thing we can do is live one day at a time and work on ourselves and our boundaries. And in time, when we're happier and healtheir, our lives will (hopefully) reflect that.
In the meantime, I agree about seeing a doctor. As Learn to Live said, having an assessment for depression may be beneficial right now as you're going through so much. In grief, we're meant to feel a range of emotions including sadness. It's just that when the depression doesn't shift, and we're unable to function on a day to day basis, we may need medical help to bring the chemistry back to normal levels which will in turn, help us cope better.
At the end of the day, what would you say to or do for your best friend if they were going through what you are? Maybe write these things down. Then, treat yourself as your own best friend. You will make it Falling...one day at a time....