Bismillahi Rahmani Rahim - In the Name of Allah, the Beneficent, the Merciful
Salaam Alaikum wa Rahmatullah
There is nothing wrong with swallowing saliva while you are fasting. To say that you have to spit is wrong. It is extremism and just plain disgusting. Can you imagine the streets of Cairo or Madinah if this were true? There'd be no dry place to walk!
When someone tells you something is permitted or forbidden, you can ask him or her to bring the proof. It is a VERY serious thing to add anything to the religion or take it away. Imagine that if you listened to this person - you would have a very hard time fasting and would become dehydrated more quickly and perhaps abandon your fast, astaghfirullah! Then the person who gave you this misinformation would bear part of the sin.
You are fasting for the first time? MashAllah. May Allah make it easy for you. Just remember to drink lots of water in the morning before the fast begins, and eat a breakfast with good protein and complex carbohydrates. This will help sustain you. Also, the whole reason for the fast is to discipline ourselves and gain reward from Allah, so you should abstain from any vain talk or bad words or bad dees. Do your best to use this time to build good habits that you can carry on for the rest of the year. I remind myself like I remind my brothers and sisters in Islam.
Fi Aman Allah,
Nancy Umm Abdel Hamid