Degenerative disc disease ftw?
Generally, it depends on what's causing the pain as regards what reduces it.
Booze is a CNS depressant. It puts a damper on everything in the central nervous system, and that includes pain perception.
Heat typically works by improving blood flow to affected areas.
So, most likely, what's happening is that your muscle spasms are caused by the pain, rather than being the immediate source of pain. The tension does make pain levels increase, but stopping that without addressing the originating cause can't and won't eliminate all of it.
So, muscle relaxers can only do so much. I would argue that they're doing something, because there's not been any cases of total immunity to any that I've been aware of, and they're a first attempt for most chronic pain cases. But if they don't target the actual cause, then they can't do enough. In other words, if the pain is causing your muscles to tighten up, a muscle relaxer is only going to partially reduce that tension because only part of that tension is involuntary.
It may not be conscious tension, but it isn't something that is caused by the muscle itself. It's a response to pain. So a muscle relaxer is kinda like a bandaid, not stitches.
Booze, however, is going to work in your brain, blocking off the pain signals, or more accurately reducing your ability to perceive them. Once you no longer perceive the pain, that part of you that's holding those muscles tight to try and prevent/reduce the oh-so-lovely pain from bulging, slipped, or herniated discs start to relax almost all the way, as opposed to the tiny bit that the muscle relaxers can make them unclench.
Now, it's important to note that the use of involuntary here doesn't mean that the rest of your muscle tension is a choice. It just means that the part of your nervous system that is making it happen is a different section than the involuntary part. Now, you can actually exert conscious control over that kind of muscle tension, but it takes effort and practice. And, it probably won't reach 100% release because your brain and body are going to resist it. Plus, pretty much the second you stop doing the methods that relax the muscles, they'll go right back to trying to keep your back immobile. So it's never a permanent solution.
The key to finding a balance often means the long, hard road of physical therapy combined with training in progressive relaxation, breath control, and all the other tools that give you the ability to intercede in the process.
Alcohol isn't a long term solution. To the contrary, the longer you rely on it, the worse you're gong to perceive the pain, and the more it'll take to get relief.
There is, however, some good-ish news. DDD is progressive. But! Most of the time it'll reach a point of relative stasis. Things will bulge and slip more radically during the early part of the disease process. At some point, it'll slow down its progression, and the changes tend you be more localized than along the entire spine. So you'll reach a point where it won't get worse fast, and will usually only get worse in small sections. I'm in that phase of things myself, and it isn't exactly fun, but it means my pain and mobility levels are stable. There's a high chance you'll reach that point too.
Once you hit that point, as long as you haven't pushed things into addiction, stuff like muscle relaxers, Tylenol and the like can keep pain levels under control enough to get by.
Until then, keep on your PT program. You want to keep as much flexibility, mobility, and joint health as possible. It really is one of those things that if you don't use it you will lose it. But don't make the mistake of doing absurd shit when you aren't in debilitating pain. You can't actually move normally, you just can't perceive all the minor injuries you're causing that make the pain worse once whatever you use wears off. That's one of the reasons I quit accepting opiates. Yeah, I hurt less, but I couldn't tell when I was doing something wrong, so I was getting worse, faster. I'm just now recovering properly from fucking my back up the last time I took some of my opiate pain meds. And that was in November ffs.
So, if you need the relief to get by, use what you gotta. Just don't fall into the trap of thinking that lack of pain means there's nothing wrong.