Sigh. I'm sorry you deal in this. I agree with you. Much too fast, and not esp considerate. She sounds impulsive. Though the roomie sounds impulsive also -- it is in poor taste jumping into relationship with your GF without talking to you about it first. Makes living together hella awkward!
All I want to do is to move on from this issue so I can get back to living life
If that is goal? GO FOR IT! Focus your behaviors on that goal.
EMOTIONAL & MENTAL HEALTH
I see it's stressy right now, but thinking hard stuff out, and feeling hard emotions isn't forever either. To improve those?
Seems easiest to break up with her, process a break up, and give yourself time to heal.
Could tell them they are free to date how they want but please tone it down around you for the next X weeks so you can adjust to your new reality. That's reasonable under the circumstances.
- That means no kissyface in front of you in person or on phone where you can hear it. Go to HER place for overnights. Neither tells you their relationship joys or concerns.
- They can kissyface and overnight wherever they want AFTER you have had you X weeks to adjust to your new reality. STILL don't be telling you their relationship joys or concerns until you feel ready/willing to hear it. (You can keep it to yourself if you NEVER want to hear it. Just tell THEM "I'll let you know when I'm ready...")
Then move on yourself to date someone less impulsive and more considerate of you when you have healed from the break up process.
Your roomie goes for your GF without getting your goodwill or blessing. If you choose to move out because of the discomfort roomie created, how's that your fault or your behavior damaging the friendship?
Figure out what is best for your financial health. Not everyone can just suck up unexpected moving. If you can afford to and if you need to do it to improve your emotional and mental health and get away from these folks, do so. If you need to stay for a bit and THEN move -- do that. If staying works out, stay.
Stick to self-respecting behavior so you aren't dinged in your spiritual health, your core values, etc.
Could call it a bullet dodged for you and steer clear of the impulsive inconsiderate people?
Not everyone you date will be a long haul runner. Dating is about finding compatible people. Sounds like "not impulsive, considerate" might be character traits you want in a dating partner.