Leslie, 120g is no where near "too much" - don't be alarmed! The amount of protein you'd have to eat to hit that 'excessive' mark would blow your mind - and render you very, very full

60g a day is considere the bare minimum a sedentary woman should eat daily. I routinely eat 175-190g a day, to give you an example.

If you're lifting heavy weights, and particularly if you're doing high intensity cardio, you can (and often should) eat 1g of protein per lb of current body weight.

HTH
Nat