Is my nerite snail sick or dying?

I am very new to fish keeping and aquariums, but I have a three gal tank with a beta fish and a nerite snail in it (plus a peace lily). A few days ago I noticed my snail on the ground with (what I think is) his trap door closed. I originally thought he was dead but he didn’t smell and I read that some nerites do this so I let him be. I immediately did a water change, and he started to move again. Two days later he was on the ground again, but a few hours later he is up and moving. His foot (is that what you call it?) looks really weird and I don’t think he is healthy but I don’t know what to do for him. Any suggestions would be welcome!

 

It sounds like he's perfectly healthy, but your water looks cloudy. Did you cycle your tank and what are your water parameters?

 

It sounds like he's perfectly healthy, but your water looks cloudy. Did you cycle your tank and what are your water parameters?

I think I cycled it, but maybe not? What would I need to do to cycle it?

 

I think I cycled it, but maybe not? What would I need to do to cycle it?

Did you get the tank and let it run with an ammonia source before you got fish, do you have a water test kit?

 

Did you get the tank and let it run with an ammonia source before you got fish, do you have a water test kit?

I got a beta and then a little bit afterwards I got my snail but that’s all that’s in my tank. (Is a plant a source of ammonia?) I do have a water test kit.

 

Update: he fell off again today. There seems to be some white on the bottom of his shell where there wasn't any before. His foot also looks smaller than it usually is, so I don't know if there's something wrong with it. I'm just concerned because I've heard of other Narites showing similar behavior and then dying a few weeks later.