With this build I finally decided to climb, from Silver IV, 4 days before the end of the season. I got an insane (for me) 80% winrate in 3 days (in 18 games, I suppose). I don't know if this build is really good or if people become crazier in the end of the seasons, so I'll just put all the info here and I hope it can help someone. o/

You'll have much less damage because of runes and starting item, so you will need discipline to farm and do not take damage. AVOID ANY ENGAGE you support try to make. You don't need early fights, just gold and stacks of Tear. You can B with 1300 Gold (T2 Boots + Long Sword) or at least at 950 for the Boots.

After 10-12 minutes you will get your Manamune, maybe Muramana already, so you'll have a powerspike to start some fights now. You can farm easily and your objective now is to kill the enemy bot lane and destroy their tower. After that probably the enemie jungler will try to help their bot lane, then you must go to other lane (mid, maybe) and try to destroy the tower too, or fight for dragons since now you have a good damage.

Now you have damage, sustain, wave clear and infinite mana. Try to wipe minions for your team to destoy towers, poke enemies away from objectives, when the towers break do a E WQ and after R... You'll be stronger than most of your enemies because Manamune and Essence Reaver are cheaper than most of early items of many champions.