Teething?

My baby is 2 months and one week old and for the most part I have been nursing her. However, when I leave her with my mom she drinks my breast milk in a bottle. A few days ago she started to refuse the bottle and only wanted my breast. I tried changing the nipple of the bottle and that didn’t work. My mom says she might be teething but is it possible to start teething at 2 months? She is also drooling a lot and is constantly putting her hand in her mouth, which I know are symptoms of teething but when I look in her mouth I don’t see anything that might look like teeth erupting (maybe it’s too soon to tell) I’m concerned because I am going back to work soon and I know it’ll be difficult if she continues to reject the bottle and only want my boobies 😞😩