Is it possible to have separation anxiety at 4.5 months old?

Sarah • Married 5/31/14 Started trying for a baby 5/31/15 Chemical pregnancy 6/23/15 Pregnant again due 3/29/16
My son Oliver has been acting strangely the last couple days. He won't let anyone but my husband or me hold him. Oliver will be completely content but when I hand him off to my sister or mom, who see him regularly, he bursts into tears. My husband and I went on a date Monday night and my dad, brother, and sister, who my son knows and has never had a problem with, cried for an hour and a half until he fell asleep. He did the same with my aunt and uncle yesterday and another aunt and cousin today. But every time, as soon as my husband or I take him back, he stops crying!