Melee Champs vs Control Mages in the Midlane?

I have been playing for about a year and have pretty much consistently kept it in the Mid Lane. I have plenty of experience in all of the different types of Mid Lane champs, but I had a question about a couple match ups I have been getting recently and wondered if anyone had any constructive input.

If I am playing a Melee champ like , and run into a control mage like who seems to take personal offense to me killing a single minion, how do I get enough CS to be able to scale enough to leave lane?

I had a game yesterday with that match up and literally could not farm. Because even standing well behind my tower, has the range to poke me and back up to not take a single tower shot. So I could not step up to kill any minions.

I tried rushing MR items like , but her base magic damage even from level 1 was doing obscene amounts of damage to me every time she hit me with that ball.

I tried killing the other JG's Rapters a couple times early game but just ended up burning because I wasn't strong enough to do it the first couple of levels, especially since I was rushing MR.

Before level 6 its also really hard to try and roam to gank with because her kill potential and gap close is almost non-existent and would just try to follow me and end up killing me if I left anyways because she was more interested in harassing me anywhere on the map than she was in killing her own minions.

Any suggestions on what to do in that situation, when you're pinned well behind tower and are getting poked too hard to be able to even be able to kill any of the minions under your own tower?

Because I was never able to catch up, even post level 6, because everyone had gotten so far ahead at that point.