Wa alaykum assalam,
Yes, there is hadith about the healing properties of black seeds (as the brother said, they don't mention the oil specifically):
I heard Allah's Messenger (ﷺ) saying, "There is healing in black cumin for all diseases except death." (Sahih al-Bukhari)
And they do have a huge amount of healing properties alhamdulillah. As far as your eczema is concerned, definitely get it seen by a doctor as well and start trying black seeds, inshaAllah it'll help sis.