The arm pain has nothing to do with your lumbar spine, but people who have lumbar disease also tend to have cervical spine disease.
You need another xray of the cervical spine.
People with lumbar spinal stenosis usually get relief bending forward, so you're going to need more than an x-ray -- you need a proper diagnosis, probably multiple diagnoses.
FInd yourself a good non-surgical back specialist and follow up. The numbness in your arm could be the beginnings of permanent nerve damage.
Best wishes/
Sometimes, this stuff JUST HAPPENS. You'll drive yourself nuts just trying to figure out what the cause is.
I'm not a doctor, nor am I smart enough to tell other people what to do.
But let me tell you, if you can find a good physical therapist (I found one trained in the Mackenzie Technique, which may or may not be good for you), you may be able to dump most or all of those expensive side-effect causing medications!
Every single atom of your body gets exchanged with a brand new atom every 7 years! Can you believe that?!? You're really young -- if you do things right, and I mean REALLY right, right now, at your age, you will be surprised what you can accomplish.
Don't ignore all of this. Don't let weeks turn into months turn into years, and then you end up some old person on a bazillion different medications, posting on forums like this about how the pharmacist won't give you your refill on time, etc., and take this bull by the horns and get a REALLY good physical therapist, get some really good advice (not cr*p like I'm posting here, no, I mean really really good advice), and make the right moves, like a big game of chess!
There's lots of positivity coming your way right now!