I don't know a whole lot about iPhones or macs, so this might be off-base, but I do know that Chrome by default will share things between phones and PCs and I've occasionally had issues where my phone and my PC got themselves set up with conflicting cookies, and once or twice I've also had something messed up in the cache. When clearing the cache didn't fix it, problems were fixed when I deleted all BGU-related cookies from the browser on my pc and all cookies on my phone. (I couldn't figure out a way to delete selected cookies in the Android version of Chrome.) Safari might be doing something similar, although if you're using a different browser on your PC the problems are more likely all on the phone.
No guarantees that it will help, but you might try this: Clear the cache in safari on your phone and see if that clears things up. If it doesn't, log in and explicity log out of the forum and "My Courses" on your phone, and do the same on your PC. Clear the cache and delete all BGU cookies from browser on your PC, clear the cache and delete BGU cookies from Safari on your phone (delete all cookies if there's no way to get to them one-by-one).