While you mention morgana, but it could be said likewise for a lot of other champs. Poppy can stunlock you into wall, cho gath can chain knockup silence, fid can chain fear silence, brand (before nerf) could nonstop stun, etc.
I always run Legend: Tenacity rune and rush tenacity boots asap, which gives you 25% + 30% + 30% (they don't stack, they act in 0.75 x 0.7 x 0.7 manner) and result in 63% tenacity, which allows you to break out of chain cc and fight back. Even easier if you buy the iron elixir later.
Back in my days, tenacity rune and rushing ten boots was a must, and it was a common sense to go clear jungle unless you have one of the following 3 abilities:
- safe waveclear
- sustain/safety in lane
- a way to fend off your lane opponent
It sounds like you were struggling against her, so I would suggest (since you can spam abilities) that if you're facing someone you don't want to trade blows early on, go clear camps, come back to clear wave when lane gets pushed to tower, repeat, get to lvl 6 first, then all in.