Thank you for your query.
Though late in responding, you have not mentioned where exactly on the body are the lesions occuring and why do you suspect them to be spider bites. What kind of discharge is coming out from the lesion? How large is the lesion? What is the surrounding area of the black head like?
If the area was large and red due to inflammation and the discharge was pus like then the use of antibiotic was appropriate.
If these lesions are appearing on the hand then one should consider that these could be some allergic reaction
to what the child may be playing with or could be insect bites
while is out playing.
I hope I have answered your query to your satisfaction.
Wishing your son all the best.