OP, if the Head has rejected your information that your child was sick and unable to attend school, then she is saying you are lying. I would be furious in your shoes and would be resigning immediately as a governor as I couldn't continue to work with a school that held that kind of opinion about my honesty and integrity. However, that doesn't help with your penalty notice issue.
I'm assuming the D&V was marked as authorised? ie they accepted the medical reason on that occasion. But as other posters have said, ,ask for a print out of the attendance record.
Our LA only issues penalty notices once unauthorised absence reaches 10 half day sessions (5 full days) in any 10 week period. I think that's a fairly standard policy.
So assuming the D&V was authorised, and in any case was over 10 weeks prior (as it was the previous term) they must have recorded the whole of the cough and sore throat week as unauthorised. IE they don't accept that he was too sick to attend school and/or they think you went on holiday (it being a Monday to Friday absence) and lied about it. That's outrageous.
So, can you assemble and provide proof that you were at home during the period (phone records, bank statements showing local spending in local shops etc)? That dispels any suggestion you went on holiday and pretended your son was sick. Which leaves the argument that you made the wrong judgment call and he was well enough to attend school. NHS website says that a child with a cough or sore throat shouldn't have to be kept off school. The school may therefore have rejected cough/sore throat as a valid reason. However, a child with a fever ie temp above 37.5 C should be kept at home until the fever has resolved. www.nhs.uk/live-well/healthy-body/is-my-child-too-ill-for-school/ If the doc prescribed calpol then I assume your child had an elevated temp for at least some of the period. Was this made clear to the school? Inform them (or reiterate) that your child had a fever - proof being the GP appt slip and prescription. At the very least, you are on firm ground that the absence on the days your child had a temperature was incorrectly marked as unauthorised. Any additional days you kept him home until he recovered properly might be more of a grey area (but wouldn't have taken you into the Penalty Notice zone, if they'd at least marked the first days as authorised).
The world's gone mad that you're being put in this position.