Sounds like a combination of factors. If you're just starting to go for longer rides, then yes, eventually you should get used to the back strain and presumably your back muscles will get stronger. You might try doing some exercises specifically to work your lower back and build some strength. I used to have a lot more issues with back pain on the bike before I started hitting the gym and strengthening my "core," aka torso. Now I don't have much problem.
But raising your seat height and not the handle bars sounds like a mistake as well. What prompted you to do that? It sounds like one of those jokes, "Doctor, it hurts when I do this... then don't do that" jokes. Why not just move your seatpost back down and make sure you get rest between rides so your back has time to recuperate? You're probably bent down too much to reach the bars. And that's not a good idea for long-distance riding. Rushing into any new regimen can be a mistake if you don't give your body time to adapt, so don't forget to rest or take some easy days in between those long rides.
I'd say it also depends on your age. If you're 21, then you'll get over it soon. If you're over 30, you might want to take my advice and hit the gym to strengthen your lower back. Strengthening your shoulders and triceps wouldn't hurt either, so your back doesn't have to do so much work to you up.