Firstly there’s the good ole opioids.
Secondly there’s NSAIDS
Thirdly there’s paracetamol (acetaminophen) which I understand to be sort of in a class of itself
Is there a fourth type of (drug) painkiller that’s reasonably effective and can be self administered?
Depends on what the source of the pain is. I was prescribed valium (anti anxiety and muscle relaxant) for pain from a disk and nerve injury. And it works quite well.
By the way this would be the benzodiazepine class.
Triptans have been used for pain, but I believe they are specialty drugs and might actually fight certain conditions that cause pain rather than dull the pain itself.
I believe that antidepressants have also been used for pain, but this is an off-label usage and thus antidepressants might not be considered painkiller drugs per se.
How are COXII inhibitors classified?
I thought that they were NSAIDS.
SNRIs can be used as both painkillers and antidepressants, Cymbalta is listed (and advertised heavily)for both. Some of them are for antidepressants only and some for chronic pain only, but this is probably more a marketing thing than effectiveness thing. Bicifadine is a new SNRI coming out, but they’re not bothering to test it for depresssion since there’s so many out there already. Note the SNRIs are for chronic pain, not “ow I got a boo-boo” type pain.
Anticonvulsants, such as neurontin, are often used for many types of nerve pain.
Dissociative drugs, like ketamine and other dissociative drugs are often used as supplementary treatment for certain kinds of severe pain. Burn patients, for example:
http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA480518
They gave me lots of ketamine in the burn unit, causing horrific nightmares and hallucinations.
I’m no expert, but I have read that cannabinoids (marijuana) block nerve pain through a different mechanism than opiates.
There’s aloe vera. I’ve no idea what class it falls into but it works amazingly well and instantaneously on burns
So, how does that work? Given the type of drug it is, I would not think it would affect pain–except to make the user just forget about it, maybe.
The peripheral nerves that detect pain have lots of receptors for cannabinoids just like they have receptors for opioids.
Opiate agonists like Tramadol are prescribed for chronic pain (I take it for an arthritic neck that shoots pain through my shoulder and down my arm for weeks at a time). These somehow feel like opiates without being opiates.
They are opiates. Don’t be fooled. They are opiates in every aspect other than a tiny, technical molecular distinction. But they do the same thing all other opiates do.
Correct.
And they also have a LOT more interactions with other drugs.
It’s a messy opioid med, it’s not a non-addicting alternative to opioids, which is what the pharma guys try to push it as.
Pain’s tough to treat. I’ve taken hundreds of Continuing Medical Education hours on the topic, and worked with and treated hundreds of chronic pain patients, both legitimate, drug-seekers, and drug-seekers who also had legitimate chronic pain. 
As far as pharmaceuticals go, I find 4 main pain drug types in my armamentarium:
NSAIDs (aspirin, motrin, naproxen, indocin, etc. etc. etc.)
Acetaminophen (aka tylenol, APAP, paracetimol)
opioids (morphine, oxycodone, vicodin, codeine, dilaudid, fentanyl, heroin, tramadol, and a few dozen others)
neuropathic pain meds, particularly tricyclics and gabapentin.
Others may have niche use here and there, but in 99.5% of the cases, those are the drugs uses as analgesics (anesthetics like topical lidocaine also may have a role.)
Ugh, off topic, but tramadol kills me. I hate seeing it on my patients’ med lists. Same with cyclobenzaprine (Flexeril). I had a patient who was addicted to tramadol. He was able to to get it through the internet somehow. Anyway, Qadgop covered it. Sorry, just wanted to vent about the tramadol.
Oh! And Benadryl!
There are also anesthetics such as lidocaine patches (or IcyHot, etc., for OTC remedies) and compound medications like Excedrin.
There’s also a new painkiller class that’s being researched, but I can’t remember much more about it, and Google is not being helpful. I think they might be NK-1 antagonists, but the Wikipedia article on them doesn’t mention their painkilling attributes.
I also found mention of conolidine derivatives, but we don’t yet know why it works, so that seems unlikely to be the one I was thinking about.
What about capsaicin?
I want to remember reading about it being used as a nonaddictive alternative to opiates.
It’s a very poorly understood medicine. It has both opiod-like effects and SSRI-like serotonin stimulation (or reuptake blockage). Without going too much off-thread; while I understand the nasty potential of this medicine, it has been nothing short of an absolute, flat out miracle for me. I stumbled upon a unexpected, wonderful side-effect of the drug that flat out solved one of the most vexing, soul-haunting, depressing aspects of my spinal-cord injury: tramadol gave me my orgasm back. It’s really a long story and not appropriate for this thread.