I have something very similar, except mine has been generally 24/7 for nearly 8 years. I also don't usually have the dizziness, but I do have the fatigue. Alcohol can make the pressure worse, but generally it's more like I have an intolerance, in that I can get very unpleasant symptoms from just a couple drinks. Certain kinds of exercise make it worse too--especially anything strenuous. Running and any kind of lifting activity seem to cause the most problems. However, walking a few miles (or more) seems to be the best--it doesn't make the pressure worse, and it just makes me feel better overall.
I know of one person who used to be here who also shares our symptoms, and she found a lot of relief with Amitriptyline. I haven't tried that drug though--for a few reasons it's not a good fit for me. I have tried Topamax, though, but it didn't help and the side effects were very annoying. The next one I'm going to try is Flexeril, probably.
lemme know if you find anything helps, or if you have any progress otherwise.