You essentially have a few options if you scout a forge fast expand.
Try to out macro them (Defensive)
You can play the long term macro game, take a 3rd and out produce him. Because he is going for an economic opening it means that he won't have a strong army so you will be free to drone hard like you say you are. However it sounds like you might be missing injects and not having enough larva to fight the protoss army. Either work on this mechanic or drop a few extra macro hatcheries so that you have some extra larva that way.
Constantly be scouting them so you aren't caught unaware of what they are doing. If you see a stargate you know they are going some type of air play and should be getting appropriate units to match once you know what they are getting (ie. know the difference between getting mutalisks or corruptors), or maybe they're just rushing carriers/mothership. Make sure you scout often because knowledge in this game is vital.
There are several kinds of pressure/all-in strategies that you can do if you scout a force fast expand.
You have your traditional baneling bust which will work if they don't have enough defense. You follow this up with lots of zerglings and destroy their workers.
There are variations of a Roach Rush designed to kill/pressure the protoss player if they get too greedy.
You can also use mutalisks to pressure their mineral lines because they will have a large amount of their defenses located at their choke point. This will leave you free to kill probes and get you another economic advantage. After they sufficiently defend this, either with cannons or blink stalkers it depends on how many mutalisks you have. There is a critical mass where you can have enough mutalisks that they will one shot cannons and they won't even matter. You should have a transition out of this.
Your late army composition should consist of infestors, zerglings/roaches, corruptors and broodlords if you play a longer macro game where you can get to these tiers of units. Of course your army composition should be reflective of what you see your opponent getting. For example, if they don't have colossi, don't have corruptors.
Targeting sentries will make your army stronger as it is a very gas heavy unit for them and will cut down on their higher tier units if they choose to remake the lost sentries. Lost sentries also mean that they cannot control most of the fight. What I mean by that is that they cannot force field off parts of your army during an engagement thus making your army weaker.
If you let a protoss get up to an optimal army composition, they will crush your army. A maxed tech protoss army will generally beat a maxed tech zerg army. You may be able to remax quicker and overwhelm them, but proper control from the protoss player will cause you to lose. A combination of storms, colossus, force fields, and archons with some zealots and stalkers plus a mothership will decimate any zerg army.