This is Flight, sort of like Dragon Prince "mage-wings":
Flight: Your arms are wings. If you are not holding anything in your arms, you can expend an action to concentrate (as if on a spell) and gain a fly speed equal to your speed. If you spend an action to do anything but fly on your turn, or end your turn without spending an action, you start to fall 100' per round. While falling, attacks on you are at advantage, your attacks are at disadvantage, any saving throw you force is at advantage, your saving throws are at disadvantage, and you must succeed in a DC 25 concentration saving throw to cast a spell.
In addition, world-building wise, air spirits attack things which go more than 50' above the ground, unless you first manage to negotiate with the local spirits.
For arms, I think you can minimize restrictions:
Extra Arms: You can hold up to 4 items. If you make an attack with a weapon in two hands or more than one weapon on a given turn, any shield you are wielding does not provide a bonus to AC until the end of your next turn. You can interact with two objects instead of one on your turn without expending an action.
This gives you some combat advantages but nothing extreme. For example, a LS+PAM build could do off-turn reactions with the polearm, while keeping the shield bonus until they did so. They could also fire a hand crossbow while using a shield.