Short answer: No.
That is because "stretch marks" are really NOT mostly due to actual tissue stretching, but instead are primarily caused by other factors. Let's explore this in a little more detail.
It is pretty well accepted by most physicians that stretch marks can be seen in areas other than pregnancy-stretched abdominal skin, such as breasts, hips, shoulders, and occasionally other areas. Any physician who has ever examined patients has also seen "stretch marks" in young women who have never been obese or pregnant, in men who have never been obese (or pregnant), and in many other areas of the body. I also operate on many gastric bypass patients who have been morbidly obese, and as they lose weight have developed loose, wrinkled, and stretched skin WITHOUT "stretch marks," so are those skin defects we call "stretch marks" actually due to skin stretching with weight gain or pregnancy, OR are we dealing with something else entirely?
Of course, slim, athletic young mothers who have never seen a stretch mark get pregnant, and end up with "stretch marks" on their abdomens, so it is entirely reasonable for them and their physicians to suppose they are due to the increase in abdominal pressure from the enlarging uterus causing these areas of skin damage. But, how do you explain these marks on men, teenagers, or women who have never been pregnant or obese?
The answer is that most stretch marks are caused by rapid fluctuations in hormonal status causing structural disruptions in the collagen and elastic content in the dermis (in certain individuals, but not all.) Hormonal status surely is in full-tilt disarray during pregnancy, right? How about puberty (boys and girls)? But if wild hormones are the cause, why does it not happen in all areas of the skin? Weight and actual tension on the skin can certainly contribute to the development and severity of "stretch marks" when they develop (again, think of the locations--pubertal boys' and girls' chest, shoulders, hips, and pregnant women's abdomen and breasts). These areas are not only awash with the massive changes in hormone status, but also growing rapidly (puberty growth spurt) or physiologically changing to allow a baby-size growth and breast feeding to occur)! Thus, it's not just hormones alone, and it's not just actual skin stretch alone. Stretch marks require a peculiar and unique combination of both hormonal status and rapid tissue growth in certain unique genetic make-ups to occur. However, skin stretch and tension alone without the hormonal rapid-change backdrop will generally NOT result in development of so-called "stretch marks."
So even though you may have HAD stretch marks, they are now removed via your tummy tuck, and your skin is indeed tight and swollen. But, unless you are having the precise hormonal fluctuations now that you had when you developed your stretch marks (pregnancy, right?), you can rest comfortably assured that you will almost certainly not develop "new ones" from your apparently nicely-performed tummy tuck! You may safely stand erect when it feels comfortable, and you should avoid sit-ups or crunches for 6 weeks to allow your muscle repair to heal fully. Skin moisturizer and ultraviolet avoidance are also recommended for best results. You look great! Cheers!