What type of pet do you have that has an aural hematoma?
Thank you for the additional information. The answer to your question is yes, you could drain it at home; however, you need to know that it will continue to refill. If left alone, eventually, the body will reabsorb the fluid, but it will cause a deformity in the ear - sometimes called a cauliflower ear. If you want the ear to look 'normal' or close to normal', having it surgically treated is the best answer. Below is a link to info on aural hematomas.
Please let me know if I can help further.