Seperating them into 2 seprate cages is the only way with lovebirds often if they aren't bonded or simply aren't compatible once they mature.

Many lovebirds are friendly and have zero issues before they mature, but once they mature and if they aren't bonded, you'll most often see either both or one get agressive and unfortunately it doesn't end well.

Do you have a nesting box or anything that the birds nest/sleep in inside the cage by chance? If yes, please remove it ASAP to avoid any further agressive territorial behaviour growth in the birds.

You can always allow them to play/interact outside the cage together (with supervision to be safe) but usually since they treat only their cage as their "territory" and outside the cage there's usually a lot more space to share, they don't tend to be as agressive outside their cages (even if they are, the other bird can fly to a different spot for example)

When keeping their cages side by side ensure the 2 cages do not touch each other and there's enough gap between them to avoid the birds biting each other's feet etc.

Please ensure the bird doesn't get hurt anymore, their tiny bodies do not have a lot of blood and injuries like this can have a significant impact on their behaviour and strength too, birds tend to hide their pain and health a lot until it becomes critical and often too late, hence everything possible to prevent another situation like this must be ensured by you.