Thank you for the pictures.
The appearance on the pictures looks like rosacea. It is also common for rosacea to be worsened by heat ad alcohol, although there are many other possible triggers. While metronidazole is the usual first-line medicine, there are a good number of people with rosacea that will not respond to metronidazole alone. There are several possible next steps, but the usual next step that I consider is the addition of azelaic acid. It also would be reasonable to consider the use of a retinoid, such as Retin-A, which has some effect on rosacea and also has activity against common acne, which is on of the common conditions that may mimic rosacea.
Of course, it is also reasonable to avoid triggers, as much as possible.
When there is a rash on the face, there should be some consideration of whether it could be a malar rash, such as is associated with lupus, but this rash does not have that appearance. It is true that rashes for either rosacea or lupus may be atypical, but the identification when it is atypical frequently involves a biopsy.
If I can provide any additional information, please let me know.