Your way of handling the situation was fine. The key to getting a more accurate determination of the melting point is to increase the temperature on the apparatus *very* slowly, so that you are allowing the apparatus to reach equilibrium at the new temperature before raising the temperature by a very little amount again, etc. etc. until the melting has been complete. If instead you are ramping up the temperature too rapidly, you will "overshoot" the melting point, and the apparatus will be heating itself at a higher temperature while the melting that started at the lower temperature is still occuring. In this case you would record a higher temperature when you finish your melting point determination that you would have recorded if you were heating the apparatus at a slower rate.
The key when you are comparing melting point ranges is you are looking to see if your m.p. range is at the literature range for the pure substance or *below*. If it is below the range it means that your substance is impure. For instance, if you had recieved an m.p. result of 117-125OC you would have concluded that your sample had impurities present.There is no way to get above the pure melting point for a substance, so if you get that result it is likely due to experimental issues rather than an interpretable cause.