You will probably have to find a laboratory that can analyse for Nitrogen, commonly called an Elemental Analyser (they do CHN and sometimes S as well, carbon hydron nitrogen sulfur). If you want organic vs inorganic N, that's a little more complex.

Phosphorus is commonly analysed by ICP-OES, as part of a suite of elements, but not usually including C, H, N so you might be paying for two separate sets of analysis. There should be someone on campus who can direct you to a lab that does such work with both types of instrument.

As to harvesting and collecting the plant material: You will need waders, pruning shears and a shovel. And a friend to help. Plastic bags for immediate sampling of the wetland plants, and a heavy-duty sieve to drain the samples. Don't store the samples in the plastic bags though - they WILL go mouldy and that's not fun.

Lots of paper bags to store and dry the samples. A forced draught oven that gets to 80C with plenty of air circulation to dry the samples. Don't pack them in tight, you will cause a fire! Once dried you will have to grind or otherwise reduce the stems and leaves down to powder form (