Going by what you've just posted it seems incredibly obvious that it's the BP. Maybe you've formulated your post wrong, but what else could it be? Your skin goes red when you use BP is what you're telling us.. so surely you've answered your own question?

Let me specify.

The first one 1/2 month i used BP, I was red as I could expect. I continued using it and eventually the redness went away. Three weeks ago, after having used the BP with no problems and seing great results for about a month, a change in the weather, where I live, occured. The temperature increased with 10 degrees celcius and it was much more sunny. At that point my chin started to become red again. I stopped using the BP for 3 weeks, then started out with a very small dosage once again a week ago. My skin reacted very bad to the BP once again.

So to specify my question(s):
Do I have to, sort of, start over with the treatment?
Or is it because of the weather change, and therefore I should quit BP?

Are you using sunscreen? This is SO important while on Epiduo! So soooo important! I made the mistake the other day by going out into the sun for 4 mins without sunscreen, and now my face is bright red. You must always use sunscreen even if going out for a couple minutes.