Kimiko

Where is "here"?  If it is a true emergency, then "here" is the appropriate place for treatment.

Your USC child can come to the US anytime, for any reason.  Sounds like there is plenty of family here to take care of him.
 
Having been deported, I don't see you getting a visitor visa.

i asked 2 times if USC 8 year old was in the US
no answer 
if child is with the husband here in the us
and they tried before to bypass the deportation to see a child for graduation ,  a humanitarian parole probably will not be approved
however,  seen stranger things happen
all she can do is apply with proofs and wait

If he needs emergency care I suggest you seek medical care in your country. To apply for any type of humanitarian waiver you will need documentation of his condition, documentation that he cannot receive the needed care in your country, and documents from the hospital in the US you plan to seek this emergency treatment from that they can provide the treatment and are willing to accept him as a patient.
Then you would file all of this with your request and wait for an appointment which might take months or a year. Wouldn't you also need a waiver for the deportation?
Doubtful you would get a visa given your history of deportation and the fact that you have a US citizen child.
Do you have someone you trust with a valid US visa who you could provide medical power of attorney to and they could accompany the child for the emergency treatment

Again,  where is the child now?
is he getting emergency care in the US as he is a USC (maybe living here with a relative)
and want to see him?
or with u and u need to bring him?
 
Emergency means "right now"
and from what we see humanitarian parole and a visa to enter is not happening fast
many from Ukraine are waiting months for this to happen even though our government says "it will happen"   but underline "not fast"

Is there a requirement that medical care can be paid for prior to visa issuance?
 
Good luck 

all u can do is apply and try
 
is the son with you outside the US?
 
have the foreign dr(s) done the work for him to get treatment in the US
u will need proof of any correspondence to validate he will get treatment here 
US doctor that has accepted to treat him
hospital where he will stay
Foreign dr saying treatment can not be done in your country
 
https://www.uscis.gov/forms/explore-my-options/humanitarian-parole