Coming from someone who mained support from season 4-5ish onwards, I can say with absolute certainty that in order to climb as a support you either need a reliable duo partner with a similar level of skill, or you need to be 3x better than everyone. You can climb with anyone in any role, sure, but some roles require more skill than others to climb with. Like if you play a carry jungler and are decent, you can climb much faster than if you play a mean lulu support. Your lulu support better be the literal meanest. As in absolutely devilish.
Support is unique in the sense that you both have the most control over the game's outcome, and the least. You have your hand dipped lightly into every aspect of the game- damage, heals, tanking, engage, disengage, vision, utility, etc., but most of the time you don't necessarily excel immensely in any single one of those aspects or, if you do, it's not enough to carry a game on its own merit.
You can enhance others' plays incredibly well, but it's more like you can make good players great and make up for maybe 2-3 out of 5 mistakes bad players make, you don't carry the entire game on your shoulders, unless you are a master of using pyke support or choose a mage support like lux, annie, or brand who are basically carries that sort of support kinda-ish.
It's also a thankless job, and if you mess up only a few times, you'll potentially tilt half or more of your team. Like messing up a bard ult or janna ult, or missing a single tornado once as janna and letting your adc die to the khazix early.
I have personally given up trying to play support, and I'm going back to top lane. At least there I can have more sway over whether we win or not, and if I mess up a few times and miss one or two spells nobody will be on my case like an adc would in bot lane.
If you're determined enough to try this, then I recommend playing heavy engage supports like leona, thresh, or blitz, or heavy disengage supports like janna or nami. Those typically help enhance teamfights and sway them in your favor more than other supports at the moment (except for yuumi, she's busted).