A 1st-2nd Cousin is an amazing match. I got lucky and found my birth father's family through AncestryDNA in August of last year. Since then I have not gotten anything closer than 3rd and mostly 4th and upward.
If you are a 2nd cousin you would share a great grandparent presumably.
I joined a group DNAAdoption on Yahoo groups and they have a bunch of search angels who are really good at helping decipher all the trees and dna information.
There is another testing company FamilyTreeDNA that is having a sale right now. You can upload your AncestryDNA raw data to them for $49 on sale from $100.
You would get new matches who haven't tested here, plus you get a in common with feature that helps sort your lists and a chromosome browser. I find it very nice to have along side AncestryDNA.
You have a very good lead, don't give up, most adoptees would kill for a match that close.
Look into the Yahoo group and the FTDNA upload if you can.
I am still learning it all myself, but feel free to email me or message me through Ancestry.