If you lose track of yourself in team fights turn on colour blind mode because it turns your health bar yellow, differentiating your champion from the rest. Also enable centre camera on champion with a button, not as a toggle, as a hold (I recommend space) and enable "champion highlight on centre" which will put a yellow highlighter arrow on your head when you hold space. When I learned how to play the game without locked screen this is how I resolved the "where am I" thing and now I still use it on occassion.
My advice on team fighting is based on an even fight (5v5, 4v4 etc). Your job is to stay safe and deal consistent damage. Your positioning is behind your front line, in range to deal damage to whatever comes into their front line. If their frontline is a tank then that's what you do damage to. If a carry steps too far forward you should target them but without knowing your limitations don't try to target them unless they're out of position.
To stay alive the only real threat to you when your positioning is good are assassins because they can get to you. You just have to respect them and play around what they do. When I team fight I am almost never looking at my champion or the champion I am doing damage to. I just attack move in random directions constantly doing damage to whatever is closest to me whist I literally stare at the champion who can kill me and wait to do whatever I've decided to about that. E.g. I'm team fighting and they have fizz. I am behind my front line, attack moving constantly on their frontline whilst staring at their fizz. I am literally waiting for him to fish me and as soon as the fish comes I am going to dodge it or flash it. If fizz steps forward or does his trident leap I walk back immediately until he trident leaps onto someone else or backwards then I walk forwards.
Chances are the assassin won't come at you from the front so it gets more tricky and more about vision / reactions but the same principle applies. You are in the same scenario as before but fizz is missing. Position in an area closest to where you have vision. Never stand near walls that have no vision on the other side. In these situations I pretty much look around my champion and arohnd the area near me as well as the minimap, so I can react to the assassin as fast as possible.
Without flash I pretty much advise not fighting when they have an assassin because the assassin will kill you if they're ahead 100% of the time unless they're an assassin who is heavily reliant on one particular ability and you dodge it.
The other two important things in team fighting are understanding when you can "over extend" to kill a carry. If your malphite ults out of vision and hits a 3 man knock up including a carry and your team immediately goes to fight. You can probably go on the carry. And by probably I mean almost definitely. In their minds they are going to be distracted by the CC, unable to deal damage and their initial response will be to flash away. So you stepping forward to dmg them is basically you covering the distance they intend to make, in advance. The other thing is knowing when you win a team fight and taking advantage of it. In an even 5v5 if your team kills their adc or mage, chances are if the fight continues happening you win. So you need to act like it. Imo the line between 0 kills and 1 kill is WAY bigger than the line between 1 and 4 or 5 because after the first kill with no response you are in such a dominant position that you theoretically can't lose from that point.