I would say yes you have made a double exposure, but i am not 100% sure.
There is nothing you can do about it if you have, Maybe it will be a happy accident and you will have an interesting image.
Because it is a cheep and simple plastic camera it may re-expose the film ( create a double exposure ) but you would be able to hear and feel if the shutter was released
I have the Lomo Diana F and it has a shutter that fires every time you press the shutter release button, time after time after time with out ever advancing the film. It has the shutter lever on the lens itself so it is slightly different then yours.
I would suggest that after this roll of film you try it with no film in the camera.
Keep the back of the camera open and advance the lever, press the shutter button while you look through the lens from the back side and watch it operate, then press it again WITHOUT advancing the lever and see if the shutter fires again. sense i do not know for sure how the shutter on this camera works so i can not answer definitively.
Try to learn as much as you can about your camera BEFORE you start shooting film to avoid wasting money.