Is there a good cure for bruised, swollen lips caused by accident?

No cure : Time will heal a bruise. Underlying factors. 1) how long ago was the accident? 2) did you go to the hospital? To keep swelling down, ice packs initially can be applied. Over the counter anti inflammatories or arnica montana. Vitamin k, a and c and bilberry extract can help. See your dentist to make sure some of the swelling is not coming from your teeth as trauma can devitalize them.