I am wondering if the problem is with your lancet "gun". I have acquired several over time and they ranged from one that was so feeble it didn't pierce my skin to one so violent I only ever used it once. I am currently using one I got free from Spirit (TEE2).
http://spirit-healthcare.co.uk/product/tee2-blood-glucose-meter/ If you order a free meter from them you will get a free gun included. Actually, the first one I got from them in that way was the feeble one, so that might suit your sensitive fingers. I then rang them to complain and they sent me free the medium strong one I now use. If you should decide to buy a CodeFree meter, that too will come with a gun, but I think it may be one of the stronger ones.