Hello,
I cannot confirm anything without examination but it does not look like alopecia aereta. It looks like temporary loss of
hair due to the boil and these
hair will eventually
regrow. Unless and until there is permanent damage to the hair follicles of hair, it usually grows back. It grows back in usually two weeks but sometimes may take 4-6 weeks. Apply olive oil and take some vitamin supplements for some days. Also eat a healthy, nutritious diet and drink plenty of fluids.