I imagine that it is hard not to blame yourself, but please don't! You most certainly aren't the cause of your mom needing to be hospitalized.
Try to focus on the positives: your mom did go in for help (YAY!), and you have learned some techniques to help yourself work through your range of emotions in a healthy way. Your mom will be coming home soon. Through your personal experience, you'll be able to relate to your mom in a new way. You two can talk to each other about the hospitalizations and share helpful experiences with one another.
Like: closing eyes and deep breathing; focusing on a leaf (or other thing) for 5 minutes; imagery; etc.
It's not your fault at all. Gentle hugs sent your way!