Thank God you followed your maternal instincts and took your little one to A+E, OP, and I hope that they're feeling very better, very soon.
Definitely lodge a complaint. All this "oh, it's probably just viral, so don't waste our busy doctor's time" bullshit is dangerous. As others have said, the receptionist has no right to start triaging patients because she's not a medical professional (being a first aider doesn't count as one, either, though I've met some who clearly think that it elevates them to the same level as nurses or GPs).
I was talking to my father this morning, who told me an absolute horror story - but it explains why things like this, especially with a baby, can be so fucking dangerous. A friend of his had a grandchild born 3 months ago, normal delivery, discharged, everything was fine. Their mother knew that something wasn't right with the baby (not her first child, so she had that for comparison). She took them to the GP. "Oh, it's probably just a virus". Mum took the baby home, but she wasn't happy. Back to another GP. "Probably just viral". Mum took the baby home again. Still knowing that something wasn't right. This went on for a few more weeks, until Mum took the baby to A+E, last week - 3 months old, so 12 weeks of life beyond their mother's womb. Mum explained to them that she kept getting fobbed off with "it's probably just a virus" comments, but that she knew something wasn't right. The baby was admitted for tests/observations "just in case".
She died the next day from sepsis.
Her parents absolutely did the right thing by their baby - it was the GPs who failed them. But now there's a family grieving the loss of a baby who it was apparently very clear that there was something (I don't know what, it's not the sort of thing you can ask a grief-stricken grandparent, is it?) burbling away that wasn't a fucking virus!
Mother's intuition is there for a reason. Babies and young children absolutely cannot adequately tell us how they feel. I remember my son having a migraine and when asked what hurt, as a 3 year old, he pointed to his knee, for example. Why did it take the friend's daughter so long to go to A+E? No clue, but probably because it's been drummed into us not to "take up valuable resources" there, especially during the winter (colds/flu season) - and I absolutely understand that if the child can communicate or its an adult with a stubbed toe. But with babies and toddlers...? Nope. Trust your instincts, always, because at the end of the day - who knows your baby better than the woman who grew it/is probably the primary caregiver nine times out of ten...?