So let’s start with this « water balance » thing. I’m inclined to say there’s no such thing based on the way you used it, but in reality, your blood needs to be kept at a certain osmolarity (particles of stuff per L of blood, put simply).
If you drink water, the water goes from your GI tract into your blood. Assuming you were already well hydrated, your kidneys immediately begin to pull water from your blood to your urine to and at the same time your cells start to suck up water from your blood (this is called osmosis–basically membranes like both sides to have an equal concentration so water will move from the dilute side to the concentrated side). It’s a give an take process and results in all compartments of your body have equal water distribution (acknowledged oversimplification there).
If you drink way too much water (think gallons), your kidneys won’t be able to keep up and your poor cells will swell with water and thus become less concentrated and you’ll die from water poisoning/hyponatremia (not enough sodium per Liter). If you get dehydrated, your kidneys greatly reduce your urine output to a minimum to keep getting rid of waste products. To keep your blood from turning to sludge, your cells expel water into the blood and become more concentrated.
OK so now to your question. Part of the « stuff » that your blood and tissues contain to give them a certain osmolarity is sodium. It is intentionally kept higher in your blood and other extracellular space and lower within cells, but that’s a story for another day (google Sodium/Potassium pump). There’s a range of sodium concentrations that your body will tolerate. To get rid of it, your body can concentrate it in basically all of your body fluids with sweat and urine being the main paths out. If you’re low on sodium, it can reduce the amount expelled these ways. But back to the beginning of this paragraph, if you consume more sodium, you’re going to have to put more water into your blood and tissues so that they don’t get too concentrated. The additional sodium in the blood also tells the kidneys that you’re dehydrated (higher stuff:water ratio) so it makes less urine and concentrates it to get rid of more sodium. This happens in all of your cells so sodium can make basically anywhere look puffy.
So now onto carbs. Glucose is stored in muscle and liver tissues as glycogen. It’s a long chain of glucose molecules and they are always stored with water. It’s not covalently attached or anything, but it’s still part of the storage process, non-negotiable. There is a maximum amount of glycogen that muscles and the liver can store though and after that, any glucose that can’t be burned will be converted to fat and the energy is stored that way (acknowledged oversimplification of lypogenesis). Glycogen storage only happens in muscles and the liver so it cannot affect your skin. Edit: it does represent several pounds of water though so you could lose weight from emptying your glycogen stores (going ketogenic), but this is truly « water weight » that will be immediately regained upon eating carbs again. /edit
Over the course of a day, the average person who is at a steady weight will oscillate between being topped off with glycogen and making some fat stores shortly after a meal, and being 1/2 full with glycogen stores and using a mixture of fat and glycogen for energy. As you burn glycogen, the water that was formerly bound will be released into your cells and if they become too dilute, will move into your blood. When you eat more carbs, the synthesis of glycogen will draw the water back into the cells from the blood. You also have glucose in your blood, but unless you have diabetes, that is kept in pretty tight control and won’t change much other than directly after a meal. Excess blood glucose after a meal is sent to 1) cells that need energy, 2) cells that can store it as glycogen, 3) cells that can convert it to fat.
Short version: As long as you’re not super dehydrated and peeing dark yellow, your « water balance » will take care of itself thanks to your kidneys, osmosis, and cellular transport systems. Some people retain more sodium and get puffier than others. If that’s you, cut back on the salt. Carbs shouldn’t make your face puffy and the only sure way to eliminate this extra water is through a ketogeneic diet where you intentionally exhaust your glycogen stores and don’t refill them.