To be honest, from the sounds of it... if his stomach bulge has moved down, I'm going to guess that's a stone attempting to pass itself. If it's around 1cm like you say, there's a chance it's not going to happen and things could get worse from here. Could you get a photo of this bulge by any chance??
I am not trying to worry or stress you, I just want you be aware and perhaps prepare if this is in fact the case. Hopefully, the stomach bulge isn't stone related.
Also, you say you're checking on him hourly and I know you are just concerned but - this might be bad. The constant opening and closing of the fridge door is one thing (I assume you have his container wrapped in a tea towel?) but constantly unwrapping the tea towel and looking it, or taking him out of the fridge to look into his container is stressful in itself. If your axie is already stressed this is not doing him any real favours. Perhaps try and limit yourself to checking on him every few hours if you're really worried.
The gill thing is generally because when axolotls are moving around there is more blood circulation so their gills go red (much like our cheeks go red when we exercise - did your axie move around a bit when you pulled his container out to change the water?) If they're not really doing much they tend to go a much more pale, almost white colour. It sounds strange if his gills went immediately white but I probably wouldn't worry too much...