First off, don't panic. Algae is absolutely normal. It grows everywhere in the oceans. If you had no algae growing in your tank, something would be very seriously wrong. Your tank is still very new and your nutrient levels are not way out-of-whack. Reefkeeping is a journey, not a destination. Settle down and try to enjoy the ride, even though it's not always a smooth one.
Second, your algae is looking very white. That generally means that for whatever reason, it is struggling. Leave it alone and observe one small area of it for a few days to see if it is actually wasting away or recovering.
Third, scrubbing your rock is a complete waste of time, and probably does more harm than good. You cannot -- I repeat, cannot remove hair algae by scrubbing the rock. In order to actually remove it you would need to remove the outer layer of material from the rock, which is not going to happen unless you're using a wire brush and taking the rock down to a pure white state.
Fourth, you can manually remove algae from areas where it's growing in large tufts. At water change time, start a siphon and use a long tweezers to grab a tuft of the algae. Twist the tweezers to remove the algae from the rock and let the siphon suck it up. This does not remove the algae entirely, but does remove the bulk of it, doing two things. It makes the tank look better, and exports all of the nutrients that the algae has locked up in its cells.
Finally, patience is key. This can be a long process, and there is no magic bullet. Grazer animals are great, but many consume algae without completely digesting it, which means they can actually help spread it around the tank. But they are still mostly beneficial. Most grazers are, however, pretty specific about what they don't like, and it seems that very few prefer hair algae as a food source.
