Try putting quotes around your site url and then search. Like: "mysite.com". If that works, it means Google is indexing your site.
If I'm not mistaken, for every search, Google will list 100 pages with 10 results on each page. That's 1000 results. So if your site isn't showing up when you search certain keywords, it's because your site doesn't rank within the top 1000 results for that keyword.
Check your Google Page Rank here:
I'm guessing you have a PR of 0 or 1. You need to increase that number.
The best way to do that would be to add lots of unique content to your site and do your best to increase traffic to your site. Start a Facebook page, Tumbler, Youtube, Twitter, Yahoo Answers, etc. There's lots of ways to get traffic to your site.
Another important step to increasing PR is back-linking. You basically need to spam your site throughout the internet. Post comments on blogs and leave your site url if the option is available. You can also look online for other site owners who would be willing to exchange links with you. Give them your link to list somewhere on their site and you do the same for them. You can also buy back-links if you want to invest and save some time and work.
Get your link out there, drive up your traffic, lots of unique original content, and Google will start to notice you. BTW, 2 months is still a very new site.