When a cut begins to heal, the first that happens is that it scabs over. Then, underneath the scab, new cells start to grow in to form the new skin under the scab. Within a few days or a week, unless the cut is very large, this new surface is fully formed. However, it is typically not matured completely. Therefore, it tends to have a reddened and maybe even slightly raised appearance to it. Over a period that can take weeks to months, the scar will gradually mature, getting smaller, less raised, and fading into the color of the surrounding skin.
However, sometimes this healing process doesn't occur exactly as anticipated, especially if the cuts were large, if there was any infection involved at the beginning, or if you picked at the scab or scar at any point. Also some people have a predisposition to something called keloid formation, where the scar tissue keeps growing and becomes very large and bumpy looking.
For these reasons, I suggest that you go see your primary care doctor
or a dermatologist
. They will be able to make sure that healing is proceeding as it should. If there is any evidence of keloid formation, they will be able to suggest treatments to improve the appearance.