Not sure on your experience, rank etc., but what you’ll find is there are plenty of characters that really annoy you. I have plenty.
Rath, Melka, Mico, Caldarius, Shane & Orax, Pheobe, and yes, Alani.
What you have to do is play cat and mouse, sometimes you you win, other times you back off. Hopefully your on a team where your team mates see things going on, help, or get a mic and team up with others. It helps.
Depending on the Battleborn you play with is to what will be a problem or not. I main Thorn, then Oscar Mike. I know which ones to run from, defend, play games with, or just damn right KILL 
It takes time to learn, bare with it.
CC items are totally useless in this game. Try boosting shield, health, health regen. Being too aggressive with damage items leaves you vunerable if your not with a mega tanky class. I actually use a shiled loadout with Thorn and Health regen and it’s now proving very very good.
Play with new items, see what fits your style, be hard to kill.
Remember, healers are hard to kill 1 to 1 unless your with a very Assassin like BB, so be a team player and practice.
Some Battleborn become more powerful as the game goes on. At level 5 when I get my Ultimate, I become very aggressive, where as early game I’m very strategic and defensive.
Know your limits.
