I guess you must be a high SR, because i'm in the 1900-2100 range and it's cancerous.
Usually I'm the only healer or tank while everyone else auto locks shit like Torb on offense.
Don't heal at that SR. Play a character that has a real chance at getting picks independently (I suggest Roadhog, Pharah or Tracer) and win by being 6v5 all the time.
You can hope that someone will gravitate to you because they think you're a smurf and start healing. If not, you'll still win most games (although you can't win them all at that rank).
I got placed into gold this season because I'd focused on playing support season 3 and went from diamond to low plat. I went from gold to master over the course of three weeks by playing mostly Pharah and Roadhog. I've seen that some people can climb as support but I don't really know how; the path of least resistance for me was to play Pharah. I had a 75% win rate until mid-Diamond.
EDIT: Also, talk to your team. I think the main thing that lower SR players don't do that turns them into better players when they start doing it is talk. Talk even if you're the only one talking. Talk even if it's just you and Lucio in voice chat.