On the 14th of January 2011, a fire sprinkler pipe burst in an adjacent apartment on the 2nd floor (we live on the 1st) flowing at a rate of approx 1100 gallons per minute. This resulted in water flowing into our apartment kitchen and flooding our dining room. After we were escorted from the premises by the fire department and a sheriff's deputy, we were allowed to return to our dwelling that evening.
4 days later they had their contracted carpet cleaning people come in and re-carpet that 2nd story apartment while we were left to clean up the mess in our home as best we could. Then they had the audacity to try and charge everyone in the building for the water that was expelled from the broken pipe.
After a few weeks, we started noticing that our children and we were getting quite sick without respite and each time we got over something, it came back about a week later stronger and harder to get rid of. This has resulted in my children having a lot more sick appointments at their doctor and as for us, Thera-flu should be paying us as a sponsor.
We went out and bought a home mold test kit and just got the results back from the lab today. The analysis states that there are 2 out of the 3 molds that were identified that can and will cause health problems in humans.
My question now is, in the Commonwealth of Virginia, do I have legal standing to sue the management company? If not, where do I go from here?

You don't need a precedent to sue for damages. Find out the limit for small claims where you are and request a form. Many areas are 5K. If you want more, hire a lawyer, or file a civil suit yourself.

First, do you have renter's insurance? Second, do you know who actually paid for the carpet replacement. Third, have you said anything to the management yet? Did you put in a claim for damages?

If you haven't reported the mold or put in a claim for damages why are you looking to sue right off the bat? You just got the results today. The first thing you should be doing is reporting it to management company and see what they do. Frankly you have no grounds for a suit until they have refused to fulfill their responsibilities.

Yes, what written requests to have things fixed have you made to the owner and/or management company?

Unless you have asked for and been denied or ignored you may not havve any claim.

Also it is very possible that upstairs was paid for by the renters own insurance.

Did you not make a claim to your own renters insurance policy ?