First of all, my little girl wouldn't hold her bottle either. What I did was put her hands on it as if she were holding it. I would place my hand over hers to hold it in place. I would do this everytime she ate. Eventually she put her hands there herself. Then I started holding the bottle at the bottom so she could get the feel of the weight of the bottle. Eventually she started holding it herself.
As far as the sippy cup goes, I trained my little girl to a straw before going to a sippy cup. I tried the sippy cups and she just didn't like them. She went for a straw first, then she went to a sippy cup. To train to the straw, I would suck on the liquid until it came to the top, then put it in her mouth. She would get the taste and start sucking. It took a little while, but she eventually caught on. When she started daycare at age 22 mo., we had to start using a sippy cup. She took to the sippy cup better after that.
I would definately get out of the house. You don't need to stay at home all the time. The library has some wonderful childrens programs. Most of them are for older children, but if you look hard enough, you'll find some age-appropriate. Also, pick up an Upstate Parent. In the back, you'll find a calender of activities for all ages.
Most importantly, don't feel alone. You have resources available that you don't even know about. It is hard being in a new place with a new baby. I've been there. Realize that no one is going to come to you. You have to go to them. But once you start taking those steps to becoming a member of the community, doors will open. I am a member of the Spartanburg Jaycees. If you would like, come join us. We meet every Tuesday night at Delayney's Irish Pub in Spartanburg at 7. It is in Morgan Square, right off of Church Street. On your first visit, your meal is free. Tonight is a business meeting, but other nights, we have games and fun activities. It is a great way to meet people and gain work experience as well. Also, we do group activities like we are going snowtubing on the 24th. Come out and join us.