Zach Bryan and Brianna Chickenfry. Neilson Barnard/Getty Images for The Recording Academy Brianna LaPaglia, a.k.a. Brianna Chickenfry, is spending time with loved ones — including her dog, Boston — after breaking up with Zach Bryan this week. While she takes a break from social media, LaPaglia, 25, enlisted a representative to post an update to her Instagram…