Trace the water pipe until you find it. It is most likely be on the outside of the refrigerator, under the sink, rather than inside taking room up and making it difficult to clean the filter if the fridge is full.
If the fridge was new to you there would have been an instruction manual and its incumbant on you to have read read it before turning the fridge on. It is also a good idea to keep a ring binder with plastic sleeves in which you can put all your instruction books for home appliances and keep it on the kitchen shelf among the recipe books, with the receipt stapled to the instruction. The make , model and serial number should also be added to the instructions and date of purchase for warranty or spares purposes. Not everything lends itself to being digital.
Why not put a bottle of water in the fridge, much simpler or boiling sliced lemons and use as a concentrate to add to water, very refreshing when cold and a little sugar is added, better than any of your commercial tinned and bottled drinks that contain articial sweeteners which are not good for you.
Its possible that the small water pipe could have been crushed or kinked reducing flow or has scaled up. If the flow has been reduced below a certain amount perhaps the fridge stops cooling it to prevent freezing. If the isolating valve is anything other than a 1/4 turn ball valve, open the valve fully, then turn it back a full turn. Each time you change the clocks, go round all your water valves and close them then open them fully then turn back one full turm. This will keep the valves free of scale.
