Hi,Dear ,Good Evening.Thanks for you query to HCM.This is Dr.Savaskar from India helping your out of the health query.
I studied your query in-depth and understood your health concerns.
-In My opinion the Cause of the lump under the eye, in referrence to the facts of your query-
-is-Chalazion-which is the infection of the Meibobian Gland at the outer corner of the eyelid and usually goes after warm compresses and anti-inflammatory treatment in few weeks time.
-It could be -
Stye -infection of the hairfollicle of the outer eye on lt side.
Treatment-
is Antibiotics-eye drops /anti-inflammatory drops / hot compresses by hot sponges for both the conditions.
-Oral Syrups could be added if the response is slow-which may be a case in your babies case.
Hope this would help you to resolve the issue with your Eye specialist doctor.
Wellcome for furher queries in this issue to HCM.Wishing a fast recovery for your baby.Have a Good day.
Regrads
Dr.Savaskar M.N.
M.S.Genl-CVTS