Check Set Of Dates For Possible Duplication Using Formula?

I have a worksheet which J3:NJ3 lists the dates for the calendar year. (Example - J3 = 1/1 , K3 = 1/2 , etc. )

A3:C3 are my headers for project information (project name, manager,etc)

In D3 I will be entering employee names. in E3 I will be entering Project start dates, and in H3 will be end dates. These dates are selected via validation lists of the dates listed in J3:NJ3, and it is set to auto fill the adjacent date range with an "X" after the start and end dates have been selected.

Now I also have another worksheet which is a pivot table that will auto update upon any workbook change, and will show each employee and all of the dates in which they are scheduled to work. I am using conditional formatting on this sheet to highlight any dates that the selected employee is double booked on two or more projects.

I want to keep this second worksheet as is, but to avoid having to flip flop back and forth between tabs to find out of someone is double booked, I would like to add a column (I) which will either say "Available" or "Double Booked" . Is there a formula that I can use for this? I thought about Vlookup, but I don't believe I know of a way to write a Vlookup formula that can check a dynamic range of entered dates. I thought perhaps a nested Vlookup/Hlookup, but not quite sure if that will work either.