Although the description of your child's problem is vague but what is understandable is that he has a deep cavity in one of his teeth and infection has spread beyond the confines of the tooth. If you realise the gravity of the situation that your son is suffering from a serious infection, you will not make the decision of the treatment based on the cost of the X-ray. Maximum treatments become costly because their conservative treatment modality is ignored by the patient for a very long time till it becomes unbearable or a very grave health risk. For example, like all the teeth cavities, the cavity in the tooth of your child also started from the size of a pin point. But it has reached this stage because a simple filling which could have been done few months back was not done in time and that is why the swelling has occurred.
Next Steps
Please do not delay the treatment further, mainly because only medications will not cure any dental infection. The problem will only aggravate further after a variable duration and the treatment might prove costlier at that time, not to mention the health risk your child is carrying every minute till the infection is not treated properly.