Haih sayang, bottle rejection ni memang biasa around this age, baby dah recognize badan mummy lebih best, so dia prefer direct latch! It's not something you did wrong, okay, jangan stress yourself lebih-lebih.
Honestly, at 3 months, some babies memang akan ambil bottle (even dengan breastmilk) if mummy tak around and hungry enough, so maybe it's worth waiting a bit longer before you force it, sometimes 4-5 months onwards mereka lebih flexible. In the meantime, boleh cuba trick seperti bottle pasa warm, pakai different person (bukan mummy), or even try cup feeding as a backup instead of bottle. But I really suggest you chat with your pediatrician or lactation consultant about this, sebab they can assess baby's latch and maybe suggest what works best untuk your situation, everyone's journey different kan. Please be gentle with yourself, burnout is real and your feelings are valid; maybe start with small breaks dulu and build from there? You're doing great, mama.