I've just had conjunctivitis and my eye was pretty red. However it wasn't very sore and has cleared up in the course of 2 days.
Last year I also got gluey eyes with no redness and went to the doc about it, and she said I might be having a hayfever-type reaction as pollen levels were unusually high. Now with all this rain that might not be the case here, but it could be an allergic reaction to something. How long are you camping for? If the eye's not sore and your vision is OK, you're probably OK to leave it. If it gets worse, you might be able to find a local NHS drop-in centre (if camping in the UK, of course!)
use tissues or cotton wool (non fleece) to bathe your eyes. Use cooled salted water to remove any discharge/crustiness. Don't use eye make up - preferably bin mascara, eye liner etc and when this clears up buy new stuff. you can use witch hazel to cool puffy eyes, when not using drops.
It could be dry eyes, which I have bouts of. The chemists have artificial tears, which help a lot. If the eyelid is swollen it could be a stye - again, there's some really attractive greasy slime you can get from the chemists to put on .