how often do you normally change the water?
The questions that mollyjean posted are extremely important to know in this case. Popeye can be cause by bacteria or even the water quality. You should try to answer all of these so we can better understand the situation
The most common cause of popeye is environmental due to excess gases in the water...how often do you change your water i a VERY important question in this case. Ammonia is not the only gas that is harmful for fish, in popeye it is often caused by excess nitrogen in the water. Too much gas pressure will cause bubbles to form in the blood and behind the eye (causing the protrusion). To fix popeye due to nitrogen change 100% of your water and keep changing it more frequently than you do until the popeye goes away. You may not have noticed it start to swell until it got really large.
now if this does not help than it is more likely that the popeye is due to bacteria, in which case there are medications that can be bought to treat this symptom. but try to figure out if the cause is environmental first! As treating with medication can be stressful and it lowers the available oxygen in the tank for your fish.
Injury can cause popeye...any other fish with your betta that may like to nip at eyes? or perhaps really sharp tank decorations?
A picture would really help especially to try to figure out the body curling cause
P.S the snail should be fine with your betta, unless you have a betta that likes to eat snails, if it's a bigger snail it should not do that though