Inductor value for power supply design
What happens if I use this Inductor in both input and output path?

The inductor you linked is 0.47 uH so, it will be ineffective as a filter but have no problems with the operating current.

I am unable to find the part number for matching the recommended
value(10uH to 47uH) in 0805 package at the input and output current
rates of 2A.

Yes, that doesn't surprise me - you'll have to choose a bigger package.