I can only imagine the pain of not knowing your family’s medical history or origins or why your mother gave you up for adoption.
DNA testing has reunited many adoptees with their birth families. Some get lucky and find their biological parents within days of their test results. Others work on it for years before succeeding. There are some wonderful reunion stories at DNAadoption.com – Trish’s story moved me to tears, as did many of the others. That web site has a tried and true methodology and classes for using DNA in these searches.
Richard Hill, an adoptee who found his biological roots, has just published an excellent two page summary of how to use DNA testing for adoptees. A great starting point, it is available at http://www.dna-testing-adviser.com/support-files/seven-guidelines-for-adoptees.pdf
Also if you have not read his autobiographical story of his search, I highly recommend it; click on image at the left to get that book from Amazon. It reads like a good mystery novel.
Times have changed now and for many it is no longer an embarrassment to have a child out of wedlock. These days an adoption can be open, which solves the medical and ancestry issues for the adoptee (see http://www.adoptionhelp.org/qa/what-open-adoption ). But back in the 1950s and 1960s, being unmarried and pregnant was a huge social stigma, so many of those women still want to hide that fact today.