How is green fluorescent protein distributed while inside an organism?
Distribution of GFP

When used as a reporter usually GFP is expressed by the cells themselves or attached to an antibody and injected. It ends up everywhere, is what I mean.

Localization of GFP

There are three solutions to the hidden-behind-tissue problem for fluorescence. 


Use a functionally 2D sample (nematodes, mouse limbs, etc)
Sacrifice the organism(if it's not dead already) and use optical clearing
Cleverness


Of these cleverness is the most interesting. Types of cleverness include time-resolution imaging(Light scatters instantly but most fluorescent proteins take a few nanoseconds to relax) to separate fluorescence from backscatter. Excite a slice of the sample and look at it from a slight angle 3 ns later, and you should see a depth-map. Repeat. 

You could also use optical tomography to essentially use computers and many cameras instead of time-delay imaging to solve for the 3d distribution of signal. Computed tomography is much cheaper, mostly because you don't need a nanosecond-scale laser + capture system(those are expensive).