But for your own peace of mind, you may want to consider buying an accurate scale.
I have a Tanita scale. It gives me the same reading multiple times in a row. Which of course now I don't need to do because I know that to be the case, so it's one time on and that's that.
For the time being I urge you to focus on your eating/exercising behaviors
. Stay with your plan, tweaking as need be, customizing it, making it more palatable and healthier as you go along. Find skills to get you through all sorts of situations - boredom, stress, parties, happiness, etc.
Focusing on the behaviors ensures that you will lose weight, even if your scale is inaccurate. Your body knows for sure what's going into it (and what's not), even if your scale is uncertain.