Same thing's happened to me, haha, support main, got placed in silver near the end of last season, had bad placement games, now I'm in bronze. I also mained supports like Sona/Janna, who don't really put out enough damage to hard-carry a game (I mean, you can do damage, I won Showdown 1v1s with both these champions, vs the likes of Lux and Kha'Zix, but you don't do that much damage when you're building as support). I've been playing mid or just filling now and learning how to hard-carry games. Honestly I'm a bit glad, been able to learn more about the game since I've been trying to get out of bronze (it is fantastic motivation to get better if nothing else), but it is a bit frustrating to crush your lane and then lose the game. I'm going to offer up some things I've learned, who knows if they're true cause hey, I'm in bronze too, but I've been finding this helpful.
Focus on objectives, map control, and learn to carry (or at least go even) in every role, since you're probably not going to get support every game. Learning every role also makes you a better player in any role, this is a team game afterall. For example, my least preferred roles are jungle and ADC, but learning jungle has improved my map awareness tenfold at least, learning ADC has helped my positioning immensely, especially in teamfights. I'm by no means good at either role, but learning and continuing to learn each role is making me a better player. As an added bonus, most bronze players only ever play one role, if you take that from them they'll just be a potato on your team. If you're flexible and can play other roles, give them their preferred role and maybe they'll go even and you can carry, lol.
I suggest trying out some new champions if you still want to play support, someone that can deal a lot of damage. I played a game as LeBlanc mid, where I crushed lane early (because LeBlanc is the most balanced champion ever, lol) but started having framerate and lag issues midway through, not to mention our Jinx was D/C for the first fifteen minutes of the game. So our botlane Annie put her carry pants on and won lane 2v1. Later when I started having issues, I would basically just try to not lag for long enough to DFG their tank and let Annie kill everyone, and we won.
Annie and Zyra are pretty common supports, and also do a ton of damage even as supports. Lulu and Karma also have great damage and utility, also are played mid-lane in LCS (more Lulu than Karma) so they do have carry potential. Nidalee spears are still scary even from a support. Brand does a ton of damage, as does Vel'Koz, especially since his base damages are so high already.
Some advice from LemonNation: If your AD is a potato, go help your other lanes out and just let your AD farm (not verbatim).
Also Nightblue3 was telling a tale of the legend of BunnyFuFuu the other day on his stream. They met in Gold at some point and started duoing, and Nightblue was talking about how BunnyFuFuu was the greatest Janna player he'd met, to the point where he could "take a potato and make them a legendary potato".
Most games can be hard-carried by a single person, in any role. Even if that's not true, I think that's the sort of mentality you need to have to get better at the game. Sorry to sound harsh but if you can't carry your way out of bronze then maybe you deserve to be in bronze (this applies to me too). If I crush my lane and still lose the game, it just means I not good enough to carry yet (or maybe I should start playing 
, lol).
On a side note, I know bronze players get a lot of flak, but don't let it get to you. Everyone was a bronze level player at some point, it doesn't mean you suck, you just have more to learn (this applies to me too).
Some last pointers: If you're not playing well or if you're on tilt, take a break, maybe play normals and learn new champions, work on your mechanics and what not
I try to think of it this way: if you can hard carry your way out of bronze, with four flaming AFK potatoes on your team, think how easy silver will be?
