First, I'd like to applaud your efforts! This is an excellent cause and I hope you can find the funding you are looking for.
I don't know if you have already gone through the legal & tax process of starting a nonprofit. If you have not, be aware that it is not an easy task, especially if you want to be an official 501(c)(3) --- which is necessary if you want to have people's donations be tax-deductible (and donors definitely want that!). You can find plenty of guidance and advice about going through this process online. There are a number of books on this topic on Amazon (including a Nonprofit Kit for Dummies!), and legalzoom.com and nolo.com provide both legal and business information.
I'm not aware of any grants for starting a sickle cell nonprofit (I'm sure you know there are already a lot of them) --- but you might be able to make use of "crowdfunding" to raise your funds from interested people through the internet. It's used a lot for people starting a business or wanting to so something artistic (publish a book, create a music cd, stage a play, etc) -- you can click here to learn more about crowdfunding. You should also check out nolo's article about using crowdfunding to raise money for your nonprofit.
Best of luck to you!