18 was long ago for me, but I use Aleve (naproxen).

The best advice I was given was to get 23andme saliva genetic testing. It is not ordered by a doctor. It costs about $200. Most people with EDS also have CYP450 abnormalities. The CYP450 are a group of genes which affect how you metabolize 99% of ALL drugs--Rx or not. It's anonymous (at least if you WANT it to be), and will give you oodles of helpful info--from disease risks to ancestory.
Lots of EDS patients have gastric bleeding from ALL NSAIDS. The collagen defect makes our intestines and other tissues more delicate/fragile. Plain old Epsom Salts are actually magnesium and soaking in a warm tub with a cup or two of Epsom Salts can REALLY relieve pain. Gabapentin (an old anticonvulsant drug) is Rx only, but very cheap and helps a lot with nerve pain. Let us know how you are.

Alieve maybe?

Like broken mentioned, a lot of EDSers aren't affected by pain medication and anesthetics. I'd recommend Tylenol over Advil, make sure it has to artificial coating or dye. If you're wanting to stay with Advil, gel caps may work better then tablets. Some areas you can buy Tylenol with codeine, which is a fair bit stronger. Other areas require you to get a prescription.

Another option to consider is a prescription anti inflammatory. If you're worried about prescription pain meds, you could try anti inflammatories. A lot of pain in EDSers are from swelling, so alleviating that will reduce pain, and you don't have to worry about pain killers.

Yes my daughter is just 17 Hun. It's been a long road. We found out several months ago that there are rx out there that can help because Fibro myalgia is often present in patients with eds. Like the above comments my daughter has found gabapentin to be very effective for pain control. Life changing in fact. Unfortunately over the counter Meds don't work for her to much. Talk to your doctor about options.

I suggest asking your primary Dr for a referral to pain management. The pain does not go away and it usually does increase with age. Those with EDS should stay away from NSAIDs. Topical anti-inflammatory meds like Voltaren gel help and Tumeric supplements can too. Soaking in Epson salt and taking an antidepressant can help as well. Good luck!!

I tend to have fairly decent results with excedrin, as long as I don't take it too often...( stomach issues) caffeine has been known to give most anti inflammmatories a boost.

I flip back and forth between Ibuprofen and Naproxen. I have an Rx for both.
*DO NOT TAKE THEM TOGETHER*

Turmeric can have some interesting side effects for some people iv'e heard. I've never tried it though.

Ibuprofen did a number on my stomach, I was up to 8 a day. I no longer take it nor the meds that my doctor was prescribing bc I got so sick on them. oxy only made me nauseous they can keep it.
It's not cheap but I have found massages to be the #1 thing that helps with Ehlers Danlos. I also use DMSO, it's a liquid that you can get at a health food store or on-line without a dx. Its made from trees so I feel it's very safe and have been using it for almost 20 years.
I'm not a doctor, this is just what works for me and is not a RX. Yes on the Turmeric and E-Salt baths, those work for me too.

PS: On the antidepressants a word of warning!

DOCTORS WILL NOT TEST SEROTONIN FIRST?! (easy cheap blood test) That is really messed up doctors hand those out like candy and most get financial gains for it!
Do not let them give them to you until they test you first. They about killed me with them. My serotonin/dopamine was perfect - a blood doctor found that out for me, I fired my old drug pushing doctors and went natural. Sadly most doctors are not knowledgeable about Ehlers Danlos. If something doesn't add up trust your gut, fire your doctor and get a new one they are like fish in the sea, plenty out there.