Very common with the use of needles, should subside after around a week. I would ice and stay away from medications, foods that causes swelling and alcohol.
For under the eye area you are mentioning how many syringes of filler did you receive? In my opinion you would need at least one on each side, probably two to make a noticeable improvement. You many have only had one injected to cover both eyes, that is not enough. It takes 6 syringes to equal a teaspoon. I would go back to the office and get another consultation to see how much is needed to correct the tear trough area.
Your cheek bones are not pronounced giving the dent effect of your face and effecting your naso folds and around your mouth. This is an easy fix with fillers. You can have surgery for cheek implants for a more permanent fix. Find a reputable facial plastic surgeon who has before and afters with lots of reviews.
From the photos shown your face doesn't appear to be much affected by asymmetry. Yes, fillers can correct and in your case should be a pretty easy fix. I would chose a longer lasting filler such as Voluma, you would only have to have adjustments for the asymmetry about every 2 years
Go for it, most ladies really enjoy having fuller lips! Swelling can be expected for several days and depending on the technique bruising can occur, but none of this is permanent. Many women go out afterwards and buy lovely shades of new lipstick!
