Dude, you should still go see your doctor. Sure, you may be feeling somewhat better now, but that doesn't mean that your pain won't come back. I know everyone's recommending subspecialists, but really any competent primary care doctor should be able to handle run-of-the-mill back pain/sciatica without having to give out any referrals. I personally manage the back pain of my primary care continuity clinic patients, and I very rarely have to send them to a physiatrist or other subspecialist (I only refer the ones with concerning exams/symptoms or those who are not getting better with the 1st line interventions). If you don't like the advice your PCP gives you, then go to a different one. The nice thing about primary care docs is that you don't have to wait for weeks to months to see them -- you can go to an urgent care clinic.
Pain specialists are nice, but they usually deal with difficult-to-treat pain, and focus in narcotics, nerve blocks, etc. Neurologists also tend not to deal with run-of-the-mill back pain. If you go to your PCP, they can at least examine you, make sure you don't have any concerning "red flags" on exam or history, then give you ibuprofen and show you excercises you can do at home to work on back strengthening and pain control. If you do have concerning signs, they can at least decide on the initial studies to do, and who the most appropriate referral will be. I understand you don't have time for physical therapy, but all you really need is one visit to your PCP or physical therapist so that they can teach you exercises -- there's no need for you to go in 3x/week.
PS -- I would certainly not recommend waiting until you start med school to figure out how to approach your sciatica. There is a problem among preclinical med students of self-diagnosis and self-treatment, which can sometimes cause more problems than it can help, and often all these things need in order to get solved is a single trip to a physician.
Okay, I'll get off my soapbox now...
