Is it just me or is Morgana mid REALLY obnoxious to deal with?

Her W in lane is so annoying to deal with as she can outshove me, deal good poke damage, and push me under my tower. On top of that, she can just W me under my tower for free. At least with Xerath and Brand's W, I can see it coming and dodge it but with Morg's W, it's pretty much an instant cast and I get poked so I can't really "dodge" a Morg W and when i do decide to trade with her, her shield blocks my spells and she can hit me with her W and possibly a Q (that has a 90% AP scaling mind you). When I do have to back after all that poke, my tower is already at 40% HP and my jungler doesn't gank when she's at my tower 24/7. The rare times a played against a Morgana mid was when I played Fizz, and Kassadin, where I just get harassed under tower. Sure, as Fizz i have my E to dodge her Q but I'm not wasting my E on her seemingly low-damage W that she can spam in lane and that poke damage adds up. Sure, as Kassadin I have my Q whenever she W's me but she can shield my Q and continue to siege my tower and i can't do anything about it as early game Kassadin. Help me on how to deal with this.