The symptoms you describe could be those of eczema or contact dermatitis. The chance that herpes starts on both lip corners simultaneously and spreads to the upper and lower lip are small. Eczema of the lips is more common when the lips are dry, so fall and winter are more likely seasons.
Eczema of the lip area is common in those who have sensitive, dry skin that is prone to allergies or have a history of eczema or asthma.
This rash is exacerbated by several things:
1. any strongly flavored or alcohol-based mouth care product, like mouthwashes with alcohol or strong mint or cinnamon flavors
2. chewing gum with strong flavors
3. lip balms, for two reasons a. they are usually waxes and tear delicate thin skin of the lips and b. they can have preservatives or flavorings that are irritating.
4. licking your lips, which is common when they are dry and irritated, but that tends to irritate the lips even more.
When the corners of the lips are cracked, bacteria and yeast that are normally present in the mouth can get into those cracks when there is some dripping of saliva at nighttime and cause more inflammation.
I recommend you see your dermatologist for proper treatment, as that may combine an anti-inflammatory, antibacterial and anti-yeast meds and that you use just plain petroleum jelly for moisturizing. This is particularly important right before bedtime. Make sure you don't lick your lips. Also, stop any mouth care products that have strong flavorings or alcohol in them, as well as strongly flavored mints or gum.
It looks like cheilitis lips or due to an allergic reaction to any of the lip cosmetics. Firstly, It can be due to vit B deficiency. Take some vitamin B complex for some days and see if your symptoms improve.
Avoid licking the lips as saliva evaporates quickly resulting in them being drier than before. Drink plenty of water and take multivitamin supplements and do not apply lipstick or other cosmetic products for some days. Use a humidifier to moisturize the air in your home and apply shea butter or Vaseline on your lips. You can also use a homemade ointment mixed from 1 tsp glycerine, 1 tsp lemon juice and 1 tsp castor oil. Spread on lips overnight, refrigerating the leftovers for future use. Eat foods high in calcium, magnesium and flaxseed oil. If a week of compresses and emollients don't help then consult a dermatologist and get it evaluated.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.
Thank you both for your extremely helpful comments. I have changed my mouthwash, stopped eating extra strong mints and only use plain petroleum jelly as a lip balm. I can now see a HUGE improvement.