Welcome to the group! Your vet's advice was good. Cockatiels will usually lay a clutch of 4 to 6 eggs, and if you take the eggs away before the hen loses interest she's likely to keep on laying eggs trying to get a full clutch.
Fertile eggs usually hatch in 16-18 days, and after about 3 weeks the hen will usually figure out that these eggs aren't going to hatch and she'll give up on them. But if she's still hormonal she might start laying a new clutch.

Fortunately there are simple hormone control techniques that work on most cockatiels, and our main website has an article about it at
http://www.littlefeatheredbuddies.com/i ... mones.html It usually takes longer for the techniques to work on a hen that's already laying eggs, but if everything goes well she might even lose interest in the eggs before the three weeks are over.
It's OK to put her food and water in their regular place; wild cockatiels have to leave the nest sometimes to get food, and they don't poop in the nest so she'll need to walk away sometimes for that too. Some tiels don't even like to poop in the cage when they're nesting, so it might be helpful to take her out of the cage sometimes to encourage her to go. Just be careful, because if she's been holding it in for a while she might drop a huge bomb as soon as she's out of the cage!
She can spend a lot of time out of the cage if she's willing to do it. Spending time away from the eggs will help decrease her hormone levels, and sitting on the eggs will help keep the hormone levels up.