Dr. Rueckl is on the right track. If you had injections performed around the eyes, then droopiness of the eyelid would be possible side effect.
However you describe your injections to be along the forehead. It would very unlikely for this to cause your eyelids to droop. However, it is quite likely that this will in effect lower your eyebrow position. Since the botox is weakening the frontalis muscle [forehead muscle] responsible for elevating the eyebrows, upon weakening, the eyebrows will droop.
Because the eyebrow is continuous with the eyelid, as it is lowered, it contributes to a "fuller appearing" eyelid which you may be confusing with swelling.
This will in fact improve. Unfortunately you will need to wait about 3 months to wear off. Alternatively, you can also selectively weaken the muscles that pull the eyebrow down to counteract the brow droop, but I wouldn't recommend "throwing good money after bad".
Wait for the botox to wear off, and then consider another more experienced injector for your next botox appointment. The amound of botox injected into the forehead needs to be subtle for this exact reason. Over treatment can cause an expressionless face and potential eyebrow droop.