It could well be amitriptyline (Elavil is the 'brand' name) - it's an anti-depressant, a tricyclic one to be precise.
Here's some bits from Wikipedia (obviously I don't use them for precise drug stuff, but for the basics they're very good):
Amitriptyline is approved for the treatment of major depression, as well as clinical/endogenous depression and also involutional melancholia or "depression of late life", which is no longer seen as a disease in its own right
Amitriptyline may be prescribed for other conditions such as insomnia, post-traumatic stress disorder (PTSD),[6] migraine, rebound headache, chronic pain, tinnitus, chronic cough, postherpetic neuralgia (persistent pain following a shingles attack), carpal tunnel syndrome (CTS), fibromyalgia, vulvodynia, interstitial cystitis, male chronic pelvic pain syndrome, irritable bowel syndrome (IBS), diabetic peripheral neuropathy, neurological pain, laryngeal sensory neuropathy, and painful paresthesias related to multiple sclerosis and at low doses as a prophylaxis (preventive) for patients with chronic migraines. ((the FM one I disagree with strongly, as it was prescribed for me and did jack squat))
I realize most of those don't fit Eli, but Elavil is usually the first medication doctors turn to in the antidepressant category - unless they're giving him a straight sedative, Shelagh, my bet is it's Elavil.
Much love to Eli and all your sick little ones - any word on Lilith?