You simply can not give parasite medicine without a fecal.
First off you need the fecal to tell you which parasites (if any) are present seeing as different parasites require different medications.
Secondly, you need the fecal done to be able to know the counts of parasites.
The majority of parasite medicine is very harsh on a dragons system, and it would be detrimental to your dragons health to give any parasite medicine without first having a fecal done to know if the medicine you are using will even treat the parasites present.
If you are concerned about your dragons health, you really need to convince your parents to let you take him to the vet.
If you aren't seeing any signs of parasites and are wanting to medicate just for precautionary reasons, than I would have to say that it would be best to not try to self medicate.
Your mind is in the right place by being concerned for your dragons health (which is a lot more than I can say about some dragon owners ) but it really is best to see a vet if you're concerned.
-Brandon