Hello hetoame: Welcome to the board. Yes, it is true that eggs have 1 carb each. But that isn't much for the punch of protein, fat and other nutrients that are packed in that neat little package. So count them.
The colour change on the stix indicates that you are in ketosis but purple isn't necessarily better than light pink. Many people lose well without ever seeing even a dark pink. I think that drinking the water all at once is probably causing that.
If you can spread it out over the day, that will be good in a couple of ways. It will keep your urine diluted so you may show smaller ketone level. It will help your body flush out the waste products from the cells on a regular basis. It will help you kidneys and liver function efficiently. It will help keep you full and not hungry. (Thirst is often misinterpreted as hunger by a 'carb lover')
Try some of these strategies for getting the water in.
Use a 500 millilitre or 1 litre bottle - buy a bottle of mineral water - instead of a glass.
Drink one of them right away when you get up, so you are ahead of the game.
Keep a bottle or container in the frig to see if you prefer cold water.
Try drinking warm or even hot water to see which you like best.
Drink water with meals instead of anything else - I add ice to this one.
Drink 1 glass or small bottle of water with every cup of coffee or tea.
Measure how much is in your glass or bottle so you know how much you are getting.
Get the kids to drink a glass of water while you drink your bigger one. It's good for them to get into that habit too.
The more you drink water, the more you will find yourself craving it. It's only the first few days that are REALLY hard. After a while you may even prefer it.
I see you have lost 33 pounds already = a great accomplishmnet. Which plan were you following to do that?