Can a child get over ptsd on their own, or do they need help with therapy and medication?

A child may have. Overt symptoms of ptsd, other behavioral symptoms &/or developmental regression after having witnessed or experienced acute or chronic trauma. See http://www. Ncbi. Nlm. Nih. Gov/pmc/articles/pmc1414752/. Symptoms may emerge or re-emerge as a child tries to process the trauma at later developmental stages, especially if child & family therapy is not instituted within 1-6 months after the trauma.
Do best by the child. Children are resilient. However, it never ceases to amaze me that some children who have undergone horrendous traumas grow to be healthy & happy adults with little or no intervention while others others who have had what is seemingly less trauma become debilitated. Trauma is in the eye of the beholder. It would be in the child's best interest to be offered professional mental health assistance.
Yes to both. Getting over ptsd by a child "on their own" is probably not "getting over it" but "not getting it". Children under similar circumstances can go very different ways and it's not easily explained as to why. The severity of ptsd is quite variable. The more severely ill need the most intervention which includes counseling, strong support from family and very often medication or hospital stays.
Probably Yes. Depends on what you mean by ptsd if its the real thing treatment is needed but about 70% of child exposed to very upsetting situations "get over it". Over those who develop symptoms of stress disorders another 15 % remit within a year. Some forms of premature treatment of stressed kids actually make things worse. See george bannano's book "the other side of sadness.".