If you can't get high speed (at least 500 MBs) with an ethernet connection, then you must have a hardware issue. I'd suggest the following:
1 ) Swap out the RJ45 cable and run SpeedTest.
2 ) If you have another computer, run SpeedTest using the same cable and connection that you're using for the Mac.
3 ) Check the Activity Monitor to be sure the CPU load and memory used is low. I don't know what the Air reports but my MBP's CPU load is almost zero at idle.
4 ) Run a disk speed test to be sure your SSD is working properly.
5 ) You didn't mention if programs seemed to run normally on your Air.
If you can't get high speed with a cable and another computer works fine at that same location then you've obviously have an issue with your Mac. Assuming you are not under warranty then I'd suggest that you do a Time Machine backup then use Disk Utility to reformat your drive and reinstall the operating system. Before migrating over your apps check the speed and see if it is high (normal). Then if the speed is okay, migrate over your apps. If the speed then drops, one of your installed apps is slowing down the system.