The usual treatment plan you'll get from your GP for mechanical lower back pain is rest, pain relief and physio if required. You've already found out over the past fortnight that it won't get better by itself, so try and take it easy (but don't completely immobilise yourself) and follow what the GP said. If the pain gets worse/spreads/numbness or tingling returns, then get yourself back there asap.
Naproxen is a drug that is used to relieve pain and reduce inflammation, and will be much better than paracetamol, so hopefully should make a difference.