I'm not sure how you can get the true fizzy drink experience without adding some form of sugar or sweetener. If you buy carbonated water or soda water and add fresh fruit or squeezed fruit juice, you're still adding sugars from the fruit (some more than others - berries would have more sugar than lemon or lime, but they still have some) and to get a decent flavour, you need to add enough fruit or fruit pulp or freshly squeezed juice that you would need to consider the sugar content if you're diabetic for pretty much any fruit beyond Lemons/limes/Grapefruit.

I 100% get the Aspartame avoidance, but Aspartame isn't the only artifical sweetener - stevia and sodium saccharin are not Aspartame - Sodium Saccharin (Splenda, or other 'yellow packets') was once linked to bladder cancer in rats but this has been deemed irrelevant to humans and is considered safe.

You could perhaps look for drinks or squashes or cordials that use Sodium Saccharin or Stevia instead? Cordials like Elderflower or lime are available but they contain sugar - it's how cordials are made. Even if you collected fruit or elderflowers or cherry blossom and made your own cordials, you would need to use sugar. You could steep fruit teas and refrigerate them, then use a sodastream to carbonate them but I have no idea whether the carbonation would affect the flavour.