Yes, the dilution involed with homeopathic remedies mean that they are very safe to use with children. The theory behind homeopathy is that like cures like, but there is only a very minute dose of the original remedy in any homeopathic remedy.
Some people find that arnica is particularly useful in treating any bumps or bruises. Arnica can be obtained either as an ointment or in pill form.
Its main uses are to help the skin to heal and also to rest and comfort sore muscles which may have been overexerted.
It can alos help before and after trips to the dentist, because it will speed up the healing process.
The only caveat when treating children is that homeopathic remedies should be used in conjunction with conventional medicine, i.e. it is important not to continue homeopathic treatment alone for too long. A doctor should also be consulted if any condition does not clear up after a couple of days or so.