Hi Danielle,
No, you're not weird! LOL.
I have a severe intollerance to heat. I live in a dry climate, and I can't even begin to imagine how horrible I'd feel if there was humidity to add to the heat! I can't tollerate temperatures above 20C or 70F. I turn my air conditioning on in the car when it's only about 15C or 60F! My husband thinks I'm nuts. The cold is fine! I actually don't mind winter, lol.
That weird burning sensation you get, do your fingertips or toes turn color? Bluish or white or purple? Do you notice this happening when the weather is cold? There is a syndrome called Raynaud's Phenomenon. Common in Fibro and Lupus. I get this.
I can't say I get the other things you were asking about. But I get two of them!