Welcome to FT! You surely are coming to the right place for info. ^
Do you still have all the boarding passes and ticket receipt for the flights? I recalled the airliners wouldn't allow you to claim miles before your joined their FF programs. However, I also remember someone saying you could, if your flights were recent enough (not sure it's 30-day, 3 month, or 6 months), and you have all the copies of your boarding passes and receipts. It won't hurt to try. But don't sign up yet! Otherwise you would miss another new member bonuses. Read on...
Since you flew UA, if you haven't signed up with Mileage Plus, you surely don't want to miss out the member-get-a-member referral bonus. I can definitely refer you so you will get another 3K new bonus miles and I get 2K. Send me a pm or email if you want to proceed with the referral.
Here's the terms of the promo I am aware of for elite members to earn referral bonuses. Your flights in March if sucessfully claimed will definitely earn both of us bonuses.
Introduce your friends, family members or business associates to the Mileage Plus program. When each person enrolls in Mileage Plus and flies a paid, qualifying roundtrip on United®, United Express® or Ted(SM) between February 1, 2006 and June 30, 2006, you will earn 2,000 bonus miles and each person you refer will earn 3,000 bonus miles.