By all means, take him to see the doctor. Hydrogen Peroxide has absolutely no healing qualities, it is only effective in debriding tissue, and is not selective, so will also debride the underlying tissue. A far more effective treatment would have been to swab it with a mild saline solution (1/4 tsp to 4 oz water). Then apply warm moist compresses.
However, if it looks inflammed, now (reddened and swollen), it should be checked out. It is normal for lacerations to have small amounts or serous (not serious) drainage (clear and no odor) but if there is any swelling, or drainage of any other color or with an odor, it should be evaluated.
In the long run, you are better off to have it checked, than to take any chances. Also, depending on the location of the laceration, there is also the potential for a disfigurement, and a child doesn't need that.