I think you need to do some basic work on yourself before you get in any new relationship-- or try and resusitate the old one. You have a lot of anger inside of you, and a lot of anger specifically directed at women. I think it is quite natural since it sounds like your grandmother is a very punishing,hostile and unloving person. You may have been loved- but it is clear you were also made to feel unworthy.
This anger has to be understood and conquered before you could be in a relationship because it will rise up again and create the same situation over and over. It's like repairing one part of a machine but not the part that connects to the rest of the mechanisms. The connecting part will keep breaking and the machine won't work no matter how much you repair other parts.
I would also advise you to leave your grandmothers as soon as you can afford to do so. She sounds like she may have a toxic effect on you and you need to be on your own and not relive childhood rejections and control in adult hood. If you must be there for awhile, build better boundaries. If she says something nasty to her, say you don't want to be in negative interactions and that you will leave the room until a pleasant or constructive conversation can be had. Just withdraw if she gets nasty.
On the other hand, if she really wants you to leave, you should start a plan about how you can do that. She has the right not to have you in her home- and in any case, the experience of being told you are not wanted is only going to make you feel bad and angry at the rejection. And anger is what you need to work on.
I hate to say forget about the girl you love,but right now any attempt to win her back, without any major changes or new insights yourself to offer, would just not work. You need to be a better you- calmer, more loving and less angry, before you can create a good relationship. Invest in a therapist or counselor and work with someone who can help you think through the things that make you want to strike out at someone who loves you. When you know you won't do that anymore-when you know you can be loving and supportive- then you will be ready to have a girlfriend again.
What you give, shall be what you receive in turn.
I don't mean to be a hardcase here and I am not judging you. This I will say first, at least you are talking about it and being very honest.
This is already in your favor. Your up-bringing does have influence over who've you've become.
Yet, having said that: because you do understand right and wrong and learning about yourself: it is within your power to be who you want to be, as it is now your fault in continuing behaving in a manner that you know is wrong.
Does this mean that you are awful? No but learn from it.
Take a break from relationships and try to work on yourself. From the sounds of it (your taking the time to think on this and being honest about it)...you are off to a good start.
Consider yourself an architect, building your structure (you) into being a structure that you can be proud of: good and strong. When you feel complete in this, you will be ready to start a relationship. Best of luck to you.
If you live with your grandmother, you're going to have to put up with it. You don't have to agree with it, and you don't have to internalize it. But it's there, and it's her house. So you're somewhat stuck.
Get counseling for your relationship issues if you have the $$ or if your insurance helps pay for counseling.
Work on getting out of her house, even if you have to not pay on your bills for a while. Then contact your creditors and work out a payment plan, or consider a bankruptcy or credit counseling, if your creditors will not work with you.
Sorry things didn't work out but it sounds like you were very selfish and immature and she decided to move on. Let her go, it sounds like you were hurtful and abusive...even cruel if you called her names etc. Get some counselling to help you deal with the issues that are holding you back in life if you really are ready to take resposibility for your behavior. Work hard, pay off your debts and get out of your parents ( or in this case grandparents but it is the same thing) and make a life for yourself. You can do it. Growing up is somethig we all have to do. Sounds like your time has come. When you are able to fully accept resposibility for yourself and your actions, you will then attract someone to your life. Until then, put your energy into developing YOU. Gppd luck.