I might be answering too soon, but you typically don't "shape" sourdough bread. The sourdough starter will denature the gluten protein in flour, which will cause it to become wetter/stickier after long fermentation times. It's hard to say exactly what happened without your exact recipe (and ideally how you created your starter-- do you feed it with equal parts flour and water by volume or by weight) and your exact procedure.
That said, I would not be concerned with the stickiness or the apparent flattening. In my experience, sourdough, even if it appears to completely deflate after being tipped out of the banneton or even when slashed right before baking, tends to make a complete recovery.
As for the shaping aspect -- If you're following a tested recipe and the dough seems sticky and unworkable, then my guess is that you aren't supposed to work it. You said in your question that you mixed the dough -- not that you kneaded it. Just transfer it to it's baking sheet (or pan, I suppose), trying not to deflate. No real shaping/kneading should be required.
If you want to make a shaped loaf for a normal loaf pan, then you probably would want to make a stiffer dough from the start. However, adding more flour AND water would just give you more dough, not make it less sticky.
As for the uncooperative, wet mess you have... if the shape it had from drying out during the cold ferment has been destroyed, I would probably move it into a normal loaf pan and put it back in the fridge in hopes that the gluten would reform and allow another rise. However that loaf will likely be noticeably sour.
One thing I'd recommend if you don't have much experience with sourdough is to look up some examples on Youtube -- That way you can see the "right" texture and the techniques they use. I'm a Chef John fangirl, but there are a number of good videos.