A player puts down a red 3 and it is my turn. I have red cards, but I also have a yellow 3. Do I have to keep on following the red suit until I have no more red cards? If so am I then able to start another colour?
According to UNO Rules:
You have to match either by the number, color, or the symbol/Action. For instance, if the Discard Pile has a red card that is an 8 you have to place either a red card or a card with an 8 on it. You can also play a Wild card (which can alter current color in play)
So you do not necessarily have to continue the color, you may change the color any time you want, even when you still have the cards of the same color as the one on the top of the discard pile.