Ezreal is fine. It's your fault for probably using his flash as an offensive move.
Red arp, blue magic resist, and yellow armor. Followed by three AD quints will give you not only higher than average defense early game, but will also allow your mystic shot to do between 70-75 damage depending on starter items. You can always get first blood. Then make sure to get 25% increase attack speed boots to further augment your ability to dish out damage, get sheen, then occulet (or if you suck rush a BT, or infinity edge with recent changes), followed by whatever defensive item you need(or both dependingly), then get infinity edge/bt and finish off with either black cleaver or another BT sword, or before the last item make your sheen into a trinity force.
Now things vary of course versus who you are leveling, but the biggest thing is that this build gets you around 300 ad, and with talents you have some natural ArP, your high AS will allow your crits (which will now be around 800-1k) to stream freely, and your ult will have a hefty amount of damage as well.
There's a excellent guide for this build but TL;DR: Change your strategy, or learn to be cautious.