I have been there several times and have had varied experience with varied GPs (ALWAYS happens at weekends!)
I was told that the red triangle definitely suggests mastitis. But mastitis can be a symptotm of something else not quite right with the feeding, and does not necessarily need antibiotics straight away. (In fact this can make things worse)
You need to clear the blocked duct, by massaging or 'combing' (sounds odd but helps) and as much feeding as you can bear . Feed from the bad side first. Take mild painkillers if you need.
Have you slept awkwardly, or worn a too tight bra, or just rushed a feed, which meant the latch wasn't quite right?
Anecdotally (my own personal observation) lots of my friends seem to get mastitis around 4-6 months, maybe they are rushing around more, or 'getting back to normal'?
Also, the breastfeeding organisations are BRILLIANT and know loads and loads and will gladly offer advice.
Hope this helps, and you feel better soon .