First, for federal tax purposes it doesn't matter what name you use, whether you register that name with your state, or if you form an LLC. In any of these cases, the IRS is going to tax you as a sole proprietor, which means you need to file a Schedule C. They consider a single member LLC a "disregarded entity", so they will act as if it does not exist in determining tax liability.
You should already be filing a Schedule C if your self-employment activity exceeds $600/year.
The question is this: Can you combine the income and expenses for both activities into one Schedule C, or do you have to file separate Schedule Cs for each activity.
Basically it depend on how close the two activities are and if you are operating them as one business. If your contract work is web related (which I'm assuming it probably is), then I would say go ahead and combine them. Many companies do consulting and also develop their own in-house stuff.
If it's contract work for manufacturing widgets, you'd probably be better off separating them unless you can show some clear connection (like, your web apps are also about widgets, and it's part of your overall widget-related empire).
Here is a good reference I found on the topic from an actual tax person: