There's definitely a huge psychological component nausea. It's one of the reasons that if we throw up after eating something specific we won't eat it again and the mere thought of putting it in our mouths can make us nauseous. It's called aversion. I haven't eaten watermelon since I was 18 for exactly that reason.
You've only just been diagnosed and are still adjusting to having a chronic illness. You wouldn't be human if you weren't having a bunch of feelings around this - a diagnosis of RA requires grieving before you can go on and right now, all these medications are a symbol of the disease. By rejecting the meds, you're rejecting having the disease. You might want to do some reading about the stages of grief (denial, anger, bargaining, depression, acceptance) - it can be helpful to get a sense of normalcy about your feelings. Because they are normal. You may also consider seeing a counselor or therapist to get some help to adjust to you new life.
Stress often settles in the stomach and it's also quite common for people with RA to have nausea and not just from the medication. In my experience, nausea is connected to RA (of course, I haven't done a study on it). Last month, I wrote a post about dealing with side effects of medications (click here) and there may be some tips in there that can help you control the nausea bit better. I was also wondering if you are eating before you take your meds? A lot of RA meds are - as you've discovered - very hard on the stomach and eating first can cushion things. As well, I recommend that you eat something every 3-4 hours - it can be a couple of crackers, half an apple, a banana - getting your stomach something to "work with" on a regular basis can keep it from the point where it feels like it's trying to eat itself. Also, what you eat in general can decrease the nausea bit - fresh fruit and vegetables are especially good, whereas foods that lean towards queasy, oily, rich or sweet can increase the nausea.
Back to the emotional aspect. Right now, you're seeing medications like methotrexate as poison, as something that is bad for your body. If you are a psyching itself out, try doing a double psych (so to speak) on yourself. Remember that these medications aren't bad. They are tools to treat your RA and by taking these medications, you are doing something good for your body, something that will help it stay strong and will limit the amount of damage to your joints. These medications will help you do not just the things you have to do, like taking care of your family and working so you can pay the bills, but also the things you love to do. Like being able to get out of bed in the morning without wanting to cry. Like playing with your kids (if you have any) or your dog. Like taking a walk on a beautiful night, dance naked in your living room and you get the general idea. You could try visualization. Sit somewhere comfortable and quiet, close your eyes and imagine the methotrexate attacking the RA, making it smaller. You are the general, the RA meds are your soldiers who go out there and fight for you to be free. It might take awhile before you convince yourself, but keep working at it. Methotrexate (and the like) do make you nauseous in the days surrounding you taking your dose, there's no avoiding that, but if you work on switching how you think about them, you may decrease that nausea. And one last thought - try taking a bit of Gravol with your meds. By attacking the problem mentally and emotionally, as well as physically, you may get further ahead.
And don't forget - your doctor's there to help you. If the side effects are making it hard for you to take the medication, there are other options. Not just other medications, but you can also switch to injectable methotrexate, which makes you less nauseous. Good luck!