Thank you for asking your query.
The symptoms you have mentioned here, getting blotchy, flushing, red rashes, hot to touch ares, dermographism, urticarias - all are part and parcel of same allergy and hypersensitivity phenomenon group called Physical Urticarias
This means your skin and body is reacting a bit hyper to external stimuli. You could be having specifically having cholinergic urticaria and solar urticaria too. Please do not get alarmed by the names. It just means your skin is a bit hypersensitive. The good thing here is that this is not serious and there will not be any long term complication.
The best treatment would be avoidance of precipitants. That means whatever things are causing symptoms you better avoid them. Anti allergic medications like Cetirizine (H1 anti histamins) can be really helpful. If its really troublesome you may need glucocorticoids after consulting an Allergy specialist.
Hope this helps