How do I carry as Draven?

I am summoner lv24, have played for around a month now and own 4 champions. I currently have Anivia , Janna , Nocturne and Draven . I will also get Fiora or Darius when the price drops to 4800 with the upcoming patch. I am more likely to get Darius, because he is more durable and although I usually prefer champions with a higher skill cap, I believe his power in team fights will help me carry lackluster teams.

As I am not lv30, I have no access to ranked PvP, but I still play normal blind-pick games. My first champion was Anivia and I considered her my main for a long time. Now I have picked up Draven around a week ago and even since the first game, I understand the mechanics well. I usually duo queue with my brother, who is a competent Alistar who synergises well with Draven's aggressive lane dominant playstyle. I play most of my games as Draven, as I believe that I perform better as him. However, I have difficulty carrying.

I usually destroy the enemy during the laning phase and they often feed me while I build a lead of several dozen creep score. Although once the team fights begin, I feel like I am always on the worse team. I do not recall a time when I lost lane or even did not dominate, as there was only one skilled Caitlyn that I was evenly matched with. I always emerge fed, and in mid game I am almost undoubtedly the highest threat to the enemy. Unfortunately, as I mentioned earlier, I seem to always have terrible luck in matchmaking and my team often loses the other lanes even when I roam to shut down enemies. There was a game where I was 16/1, but it ended as a loss at 24/6 because the enemy Rengar focused me down while ignoring team fights. I also just lost a game 20/10, because Blitzcrank would pull me into 1v5 situations every few minutes. I am always fed, but I am usually unable to carry games. I have won games 8/0 and 17/2, but my win rate is still far below what I feel it should be considering my average KDR being 2.3. I require advice on how to carry games, as even though I am improving, my win rate stays the same even though my kill/death ratio is ever rising. How does one carry games and deal with crowd control? I might consider taking Cleanse instead of Heal if it does not weaken my laning phase too drastically.

Now this could be luck, as it is a 50/50 chance if you are put on the winning team, but this obviously sways depending on performance, as a player that goes 20/0 is far more likely to win than a player that is 0/20. This could be that I have only played roughly 30-40 games and that luck is not on my side, because I believe that I consistently am the best player on my team. Please, would someone give me advice on how to carry.