Thank you for your question. I typically focus my aftercare on restricting activities that make you hot, sweaty or flushed: Examples include strenuous activities, alcohol, saunas, hot baths, etc… This will increase your chance of bruising. If no bruising, by the next day, the you should be good to go. If there is, then I recommend another day to make sure the bruise is not getting worse. I am not as worried about the not laying down after four hours.
While in the past it was recommended that you not lie for a few hours after your treatment, the risk of migration is so minimal that I wouldn't be concerned. If you haven't notice anything unusual then you should be okay.
Most likely laying down will not have any affect on your Botox results. We do generally recommend not exercising or putting pressure on the injected area for about 4 hours after the treatment to see best results. You can call the doctor who did the Botox injections to put your mind at ease if necessary.
when Botox first got approved for cosmetic use the FDA-approved instructions incouded telling patients not to lay down afterwards, or bend over. About 10 years ago, at a National Education Faculty meeting, it was deemed unnecessary by a consensus of trainers such as myself. The only thing you should not do afterwards is rub the injected areas for 4 hours. This is to avoid permeation into the eyelid muscles which can cause a droopy eyelid.
Staying upright, no exercise, contracting the facial muscles...these are all recommendations post neurotoxin treatment. I can guarantee patients receiving Botox and Dysport treatments forget to do these things all the time and still have fantastic results. I do recommend strongly no direct pressure on the treated area, no facial/massage in the 24 hours after receiving a neurotoxin treatment. This allows the product time to settle into the muscle without manipulation from extrinsic factors. I'm sure you are on your way to a softer, smoother, more rejuvenated you!