I am 57 years old. I used to have a mild sexual urge, having sex no more than 2 times with my wife per week. But recently my sexual urge is getting stronger. In the past 7 days, I have had sex four times in addition to 2 times of masturbation when my wife is not interested. If I don't do it, the erections will keep me awake and miserable. I am worried I might be having a too strong and abnormal sexual appetite.

I would say what ever floats your boat is fine and normal for you, I would I guess be concerned that they "keep me awake and miserable"
And as long as your wife does not mind every other day or every day, then it is fine, You do need to discuss her desires and needs and at times masturbation may be the answer. Many men your age masterbate every day. Others have sex twice a year.

As Fr_Chuck said, there is nothing wrong with having sex every day (as long as your wife is interested) or masturbating. 'Normal' is different for each individual and can change as we go through life.

That said, this appears to be a sudden change and you seem to be experiencing some discomfort which are reasons to examine and find the cause(s).

I would begin by getting a check-up to make certain you aren't experiencing any changes in your health or side-affects/interactions from medicines.

Have there been any changes in your lifestyle or environment such as eating healthier, exercising, children out of the house? A healthier lifestyle and 'empty-nest' can have a major affect on a person's libido and ability to have sex.

As a wife, I will caution you to think about quality over quantity. You don't want to forget about her needs while trying to take care of your own. You may be having an easier time getting an erection, but it does not change her need for mental stimulation and affection. You don't want her to start feeling like all you want is 'relief'.

Thank you both, Fr_Chuck and Cat1864 for your opinions and suggestions.
They set my mind at ease and remind me of the necesscity to think more about my wife's mental health than my biological needs. I will go see a doc if things go on like this for another week.

Plus your wife is most likely post-menopausal and that will affect her readiness and ability. Vaginal walls thin... dryness becomes more pronounced...