What? Eve is total garbage. Also, the recent nerf hit her REALLY HARD, it was not a small nerf, it was a massive one. If you really do struggle against her though, pick runes for movement, and/or buy faster booties.
She 100% relies on closing the gap on you with her own runes/boots (and generally only gets one or the other). The key is she has to start W which telegraphs that she's near, and you can start running, then she has to get in W range and hit after it finishes and points out her location, so she either gives it away getting too close, or waits for it to finish which points at her and shes a bit out of range when it happens. In short, if you have even close to her movement speed, she just can't close that gap fast enough without flash or ulting backwards into you (using her ult as a flash doing 0 damage, which she will almost never do), to top it off, if she does miss her first Q it'll slow her movement, she can only maintain speed on secondary casts.
Basically, she's total trash but IF you really struggle against her just get the same rune as her that increases movement speed, or even the in combat speed boots should be enough to keep just ahead of her. I mean it'd suck to have to rely on doing that, but it will be reliable and should ease your current pains.
Did I mention she went from trash tier that only did well at top ranks due to allies knowing how to play around her to complete garbage with the nerf? Seriously her clear speed is so bad she doesn't even feel like a jungler after the nerf. She already is bad against Dragon/Baron (the worst JG in the game by far against them) but now she's also bad at clearing.
TBH I wouldn't worry about it, I doubt you'll see her again.