Welcome, mamaD.
I'll give the most abbreviated version answers I can, for someone who may prefer that.
1. Your neuro doesn't have to prescribe this?
Not necessarily. Your GP is more likely to be aware of this drug, as well as its safety profile. I would still come prepared with information from the Low Dose Naltrexone site (which means you SHOULD read and understand this information).
2. Any sides?
Start off slow at 1.5 mg, then 3.0mg, then 4.5mg. Side-effects are normally very minor to non-existent when gradually increasing dosage.
Can have slight “rush”, headache and/or nausea the first week or so. Make sure to take it down with a glass of water.
MAY 'stir up' MS symptoms initially (usually no more then 3 weeks), while your body attempts to *re-boot* (lack of a better word).
May experience "lively" dreams; most often a temporary side-effect. Not scary though, like some antibiotics are. 
If side-effects become troublesome upon increasing dosage, go back down for a week or two, then try again.
NOTE: LDN IS NOT TO BE COMBINED WITH NARCOTICS, CODEINE OR CRABS.
3. Cost - more or less than Tysabri?
Tysabri is $50,000 - $100,00 a year. LDN is about $10 – $20 per month (but sometimes not covered by your insurance.)
4. Really can notice changes? That is exciting.
For me (almost 18 yrs into the disease; RRMS):
- spasticity PAIN, gone
- claw hand, gone
- fatigue, improved
- better attitude and energy levels
- bladder/bowel function, improved substantially
- able to go off antidepressants (lost 30 lbs)
- take NO other symptom mgmt drugs, except occasional Naproxen
- reduced EDSS (disability) by one point in 9 months
- remained disease progression stable
- have had one attack in 3 ½ yrs, due to an untreated infection. (Was experiencing 4 attacks per year when I went on LDN)
BTW, LDN
can be combined with Copaxone (if desired), and is being used "off-label" for MS. Discuss your current meds with Skip of Skip's Pharmacy in Florida. He is GREAT at explaining things, and most experienced at compounding it.