Facing a task with no tools and no knowledge would get most people down, I think, but not you. I must salute your buoyancy of spirit as you proceed into the unknown with a light step.
A protractor is probably the wrong tool. You can perform a simplified level survey of your yard using an inexpensive laser level (I see a cheap one in Amazon for 12 bucks) and something like a yard stick. An assistant would also help.
Set up the level on the highest part of the slope. Call the spot where you place the level your benchmark. Now locate various spots around the yard where you’d like to measure the elevation relative to the benchmark, and measure the offsets of these spots say, south and west (or whatever makes sense) from the bechmark so you can plot them to scale. You might want to number or otherwise label the spots where you will read the elevation so you can record your readings in a log.
Now once the laser is leveled, note the distance above ground of the laser beam at the benchmark. That’s the height of the instrument–bechmark (elevation 0) plus the distance above ground. Now have your assistant stand at each measurement location holding the yard stick on the ground, Shine the laser on the yardstick, and have your assistant read the height of the beam. For each location, height of instrument minus the yardstick reading equals the elevation of the location. Just note the the yardstick height for each spot in the log. You can calculate the actual elevations relative to the benchmark back in the office, say, on a spreadsheet, and then plot them in SU.