In reply to CallumKX: sounds like climbing a lot will help the most. You'll learn a lot of movement skills in bouldering, really concentrate on how you move when you're warming up, try and make very movement as 'easy' and efficient as possible. When you're warmed up start trying harder boulder problems, if you can't do something try it again but think about body position and footwork and how it can change to make the move easier - it'll teach you a lot about the subtle techniques.
I don't like 'rainbowing', the great thing about indoor walls is that specific movements can be set and learnt and you lose this.
Mostly indoor walls aren't very tall, but if you find that the reason you're falling off the harder grades is that you get too pumped maybe try some 4x4s (lots of info on the internet) or climb to first bolt, clip, climb to the bottom foothold, back up the second bolt, down to the last foothold, third bolt etc.
If you physically can't hold/do the moves themselves, go back to bouldering. Hangboards etc might see like a quick fix at this stage but I'd wager the safest and most beneficial way to get stronger and have better movement is actually climbing.
When you climb routes make sure you 'plan' them before you set off, identify the crux/es, look where you can potentially rest and where you can clip the bolts in the most efficient manner. Lots of indoor routes have good holds near the bolts for example, don't waste energy holding bad holds in strenuous positions.
Redpointing (trying a route over and over until you can do it) is good, but don't get stuck on it - lots of mileage on different angles and styles is the name of the game.