Based on your description and the photos, it looks like your baby has a rash that is spreading at the neck and also pimples are appearing on the back. Rashes in this age group are common, often caused by heat, friction, drool, or irritants, but sometimes they can be due to infection or allergies.
My opinion:
The rash appears to be in the folds of the neck, which is a typical area for heat rash (miliaria), drool rash, or even irritant contact dermatitis due to trapped moisture. Sometimes, a secondary infection (like a mild fungal or bacterial infection) can develop if the skin remains moist and irritated for a few days. The fact that coconut oil and baby lotion haven’t improved the rash suggests it is persistent and may need a different approach.
Next Steps
Gently keep the affected area clean and dry. Avoid heavy oils and lotions for now, as they may trap moisture.
Use a soft cotton cloth to soak up drool and moisture around the neck often.
Dress your baby in loose, breathable cotton clothing to avoid trapping sweat.
Avoid any new creams or home remedies until we know the cause.
If the rash becomes red, swollen, oozes pus, the baby develops a fever, is very irritable, or the rash rapidly worsens, please see a doctor urgently.
If the rash does not improve in 2-3 days, or if you notice any changes as above, I would recommend an in-person appointment for direct examination and possible prescription medicine.
Health Tips
Avoid scrubbing or rubbing the area which can further irritate the skin.
Change the baby's clothes and bedsheets daily, especially if they get wet with saliva.
Watch for any signs of infection: yellowish crust, spreading redness, pain, or fever.
Do not use medicated creams (such as steroids or antifungals) unless prescribed.