Animation retargeting bends my character's arms weirdly

Almost always a proportions mismatch. If you animated on a blocky R15 rig and the character wearing it is Rthro or a different body type, the same joint angles land on longer limbs and the arms come out bent. Animate on a rig that matches what your game actually uses, or lock the avatar scaling in Game Settings > Avatar so everyone is the same shape. Also double-check it isn't an R6 animation on an R15 rig, that does it too.