Why are my eyes always puffy when I wake up in the morning? Also why do my eyelids look swollen when I wake up as well?

The puffy eyelids that you're experiencing in the mornings occur from normal fluid shift in the body from laying down to standing up. Picture allergies were under control along with a low-salt diet. Eyelid surgery was performed when this has  become more permanent.

Fluid shifts happen at night while sleeping. In the morning, the eyelid tissues will harbor some additional fluids which will present itself as a mild swelling. This usually normalizes after an hour or so. There are conditions which excessive chronic swelling of the lids but what you are describing appears within normalcy. 

Thanks for the question, this is a very common way patients come to the office seeking surgery, the puffiness is usally fat sticking out from inside the eye where normally its tucked in tight, swelling can be do to excess skin or muscle or fluid collecting in the muscle and skin, see a local surgeon for treatment options