The best is to take out all of his turrets 1 by 1 every time he try to put one. Another thing which is really efficient is to variate your pushing strengh as much as possible. If he's close to his tower and he start dropping his turret and suddenly you give up pushing your wave and force it back toward your tower, he will lose those turrets and need to rebuild is base again.
Since you complain about being a melee, you probably mean top heimer ? honestly, there is very few decent top heimer player. They tend to keep their full glass cannon build and will bring nothing to a teamfight, stay calm build tanky and you'll win later in teamfight.
Remember that Heimer can't really help but to send the wave of minions right back at you. In the worst case, just farm those quietly. You might be raging because he turrets make him safe to farm and near impossible to gank but farming right in front of his turrets his also quite as safe. Since it's out of his turrets, heimer can't do much then hitting you with a grenade if his jungler come to gank you. If you dodge it, it gonna be a 1v1 vs their jungler. So you're pretty safe yourself.