I can relate to what you're saying. I'm 26 and I've got Wegener's Granulomatosis, a rare autoimmune system disease. I've travelled quite a bit and for long stretches (longest = 1 year) and it's possible - you just need to take some precautions. Get yourself a medicalert necklace, be aware of any medications you may need and take some along if you might not be able to get them, have a backup source of funds to cover medical costs, flight home, etc, and be aware that travel insurance doesn't usually cover "pre-existing conditions" - I got around that because my condition returned in a way it hadn't manifested previously, so you probably could, too.
Know the medication side effects, make sure you get plenty of rest and if you're body tells you to take it easy for a bit, listen! And I would recommend going to the less developed countries first because in your case, it sounds like you're healthy now, so get while the going's good! Take along some antibiotics, too, because colds etc tend to trigger flares - Zithromax is a good one. Wash your hands lots to avoid germs and take along an antibacterial handwash, although those don't really do too much. (That's definitely not advice for healthy people because antibacterial stuff promotes virulent strains of bacteria!)
And sometimes it helps to be open with people - I don't drink while I'm on meds, and sometimes I really need to get to bed early, so people are more understanding if they know. You can't tell I'm sick, either, so it can be frustrating when I'm not feeling 100% because they have no idea.
You know, MS has so many different degrees of severity, you might have no problems at all! But just be prepared, and if you do have problems, it's not the end of the world (just a slight modification!)
Trust me - I was supposedly in remission when I went off to Australia (I'm Canadian) and I had a big flare 3 months into the trip. I went back onto the chemo (immunosuppressants) plus prednisone and some other nasties. I didn't lose my hair, didn't get too nauseous so I was pretty lucky, but I had lots of trips to the doctor and med costs. And one of the side effects of my meds is that I need to drink lots and lost of water so I had to be quite creative with toilet breaks! It was a wee bit stressful, too, but I ended up staying a year and I had a great time, so it didn't stop me!
I'm off to school in London, England in the fall, so I'll be away for another year and while there, I plan to do more travelling on the continent as well as Turkey and the Middle East, so I haven't let it get in the way of my plans. Sometimes the disease feels a bit overwhelming, but if it wasn't this, it would probably be something else.
And the "what if's" will always be there - for me, it's what if the disease wrecks my lungs and kidneys, what if I need another throat operation, what if I wind up with leukemia or bladder cancer... Conquering the "what if's" is a mind game - none of that's happened yet, so I just try and take one day at a time, with a few precautions thrown in.
So good luck, take care of yourself and have a fantastic time!!