Assalamu Alaykum,
Thank you so much for sharing your dream with us. Before we look into the meaning, it is wonderful to remember how special good dreams are in our faith. Our beloved Prophet Muhammad (peace and blessings be upon him) said that when the end of time approaches, the dream of a believer will hardly ever fail to come true, and that a true dream is one of the forty-six parts of prophethood. Seeing a dream like this right before Fajr is also a very blessed sign, as dreams at this time of the night are often the most truthful.
You made a very smart observation when you woke up at 3:00 AM and wondered if you were just physically thirsty. Sometimes our body's needs do show up in our sleep. However, since you went back to sleep, saw the exact same dream again, and woke up not feeling thirsty at all, this indicates that it is a true, meaningful dream (Ru'ya) rather than just a thought from yourself.
Since it is a positive dream for you, MashaALLAH! In Islamic dream interpretation, clean and clear water is one of the best symbols you can see. It represents pure faith (Fitrah), beneficial knowledge, good health, and lawful (halal) blessings coming into your life. Because you are a young, unmarried woman of 20, drinking several glasses of clear water is a very hopeful sign for your future. It points toward a peaceful and happy life ahead, ease in your daily matters, and it can also signify a blessed, righteous marriage or success in your studies and personal growth.
Seeing yourself drink specifically three glasses in the second dream could simply mean a complete and satisfying measure of goodness, as doing things in threes, especially when drinking is actually from the Sunnah of our Prophet (peace be upon him). It may also point to three specific blessings or wishes of yours being fulfilled, or good news arriving for you after a short period of three (whether days, weeks, or months), though only Allah knows the exact timing.
According to the Sunnah, when we see a good dream like this, we should praise Allah (say Alhamdulillah) for it and only share it with people who love us and wish us well.
To bring these blessings into your life quickly, I would gently advise you to stay regular with your five daily prayers and make plenty of dua. Also, try to make a habit of reciting Darood Shareef throughout your day. Reciting Darood Shareef is a form of Sadqa (charity) in itself, and Allah showers tenfold blessings and peace upon whoever recites it, opening the doors of goodness for them.
May Allah bless you with the best of this world and the Hereafter. Ameen!
Allah knows best.