This is possible, but if you ask me, I do not like to use human blood in the preparation of blood medium, due to many considerations ... It is preferable to add the blood of horses or sheep. If you want to use your own blood, you can after drawing the blood, add 1 ml of sodium citrate to every 5 ml of blood, as an anticoagulant, and, then this medium was prepared by suspending 37g powder in 1 liter of distilled water, and dissolved completely by bringing it to boil with frequent stirring, then sterilized by autoclaving at 121°C and 15 psi for 15 minutes and then cooled to 40-45 °C in a water bath. A 5% blood was added and mixed gently, then the medium was poured into sterile Petri dishes, and let dry. Finally,

the medium was refrigerated at 4 °C until use

That is possible, but why is human blood specifically and it is possible to use animal blood despite some differences in composition, number of blood cells and blood content of nuclei

To prepare a blood agar, the first thing you must keep in mind to use sterilised materials. Blood must be drawn in a sterilised tube with anticoagulant. Prepare the agar or NA as per your need following the general sterilising protocol. When the medium or agar has cooled down to around 40 degrees Celsius, pour the blood (5-8%)to it and mix properly. And then prepare the plates. It would be better if you use sheep or goat blood.