Ranged carries are fun to play because they pump out amazing damage and rack up an enviable body count, earning them all the glory at the end of a match. However, that awesome offensive power needs to come at a cost, and that cost is defense. As Miss Fortune or a similar champion, you will be easy to kill, so you need to exercise caution when engaging and keep an escape route open at all times.
If you truly enjoy this role, then my suggestion is that you continue playing it and simply work on playing a tighter game so that you take less heat. The benefits to doing this are that you can continue playing your favorite champions and the role that you love, and you will become a better player by forcing yourself to learn and improve your game instead of just switching to a champion that will be more forgiving of your mistakes.
However, if it is your desire and preferred playstyle to be aggressive and get into as many fights (and come out the victor) as possible, my recommendation is to try out a tank.
Like you, I started out playing ranged carries. I didn't do very well with them because I like to play aggressively, and so I died a lot and didn't get the level lead that a carry needs to wipe the floor with the enemy team. My more experienced friends suggested I play a tank, but I didn't want to for the longest time because tanks don't get the glory that carries do. They usually get assists instead of kills, since their role is to protect teammates by taking aggro for them, not killing things.
However, I have taken up tanking and found that tanks can be a lot of fun, because they have high sustainability (i.e. the ability to keep playing without dying or having to return to base to heal/shop) and can play very aggressively. Many of them have very fun abilities as well. I have been playing Shen and love using his ultimate to turn the tide of a battle. I don't know if Alistar is a true tank, since I don't play him, but he is at the very least a bruiser and excellent lane pusher (his heal will heal nearby minions, too!) and can be built tanky, which allows you to play aggressively. If you don't already have him, you can get Alistar (and a cool skin for him) completely free by subscribing to Riot's YouTube channel. Since you don't have to spend RP or IP to get him, it's totally risk free to try him out, so you might want to for that reason alone!
The thing about tanks that you won't like is that their damage output is very low compared to what you're used to playing as a ranged carry. However, that doesn't mean you can't thrash your enemies if you play your cards right. I've gotten 11 kills, <3 deaths, and >10 assists in a match with Shen, and saved teammates' butts with my ult on multiple occasions. I might not get recognition from them for it, but if I have a good game like that with Shen, I always walk out feeling awesome.
Ultimately, you should play what you want to play and focus on being good not just at playing the champs you love, but at playing the game in general. Farming, map awareness, positioning, and other basic concepts like these are essential to victory at high level play, and the earlier you start focusing on these things, the better off you will be in the long run.