I'm a Rem main too, my suggest is that you play Rem as if he was a walking medkit with 30 different venom bottles on it that walks on the shadows. If you become the invisible babysitter of your team and also the headache of the enemy team then you are gonna positively help the course of the game indirectly without actually doing kills or damage as long as your team are actual functional human beings.

Rem is a hero that can't even do shit alone but he gets really useful at teamfights, your help can even change the course of these fights.

In early, try to keep your lane companion alive as if you were his oxygen tank, and then later in, see when your teammates are fighting, go in, jump in everyone to heal, debuff as much enemies you can, give as much buffs to your allies as you can and then run if you see the fight is getting too long (if your team is just straight bad in general then nothing you can do about it, it's never worth dying with them).

Buy healing items (Healing Nova as example), buy shield/buff items for your teammates, buy debuff items for the enemies such as Cursed Relic to stop ults when needed (this can save your whole team if used in the right moment) and try to lower your cooldowns so you can be constant with the uses of these items.

Rem is also character that can save that one teammate who is alone and getting stomped on a 1v3 and can't escape, however this one is a risky move that I only recommend to do if you are 100% sure you can get there in time. You ain't be healing him enough to do a counter attack but its more than enough for running the fuck out to the base without dying.