If I toss a fair coin in real life and I get two heads in a row, does that change the probability of getting one tail in every two tosses? I know this sounds pretty stupid, but this is bothering me for a while. I mean, shouldn't I get alternate Heads and Tails for every two tosses I make? Or do I have to continue tossing up to infinity to get an equal probability of heads and tails?

Getting two heads in a row does not change the probability of getting a tail. There is a 50/50 chance for both heads and tails each time you flip a coin, because there are two possibilities each equally possible. The 50% probability of getting a tails is not a guarantee. It's possible to get more heads than tails, or vice versa. What the probability means is that on average the results are about equal, and you have an equal likelihood of getting either result.

Mythbusters has an episode on this, actually. They explain it really well. I recommend you watch it.