Hi Jesse,
Don’t stress! It happens. Soldering mistakes are just a part of soldering. Can you send us a picture of the board as it is?
There are a number of image sharing sites available, one of the most common is imgur : https://imgur.com/
You can upload a photo there and share the link in a reply for us to take a look. If that doesn’t work, let us know.
In general though it’s very hard to do so much damage that you can’t undo it. Even in cases where you accidentally take a pad off, as long as it’s a through hole there should be one available on the other side and a good solder joint can still be made.
Some tips for removing solder/reworking:
The solder sucker works best when there’s a decent amount of solder to “grab” onto, or form a seal. When removing solder, it’s usually best to add a bit more first. Then you want to make sure the solder is thoroughly melted, going a little bit hotter here than the initial work can help with that. You really need two hands for this job, so make sure the board is secured somehow. If you don’t have any way to clamp it, then try using some tape to tape it down to a table or work surface.
My process for removing the solder would be as follow:
1. Secure the board so I can use both hands freely
2. Apply fresh solder to the joints that I wish to remove, adding maybe a bit more than usual if I’m having trouble getting in with the solder sucker
3. Turning the heat up just a touch on the iron, heat the joint you wish to remove the solder from and hold for a couple of seconds after it’s fully liquified
4. With your other hand, bring in the solder sucker quickly as soon as you pull the tip of the iron back. Try to push the solder sucker tip down so it fully covers the joint and forms as good of a seal as possible with the PCB
5. Immediately release the piston to suck up the solder
6. Repeat steps on remaining joints until the majority of the solder is removed from all connections (you likely won’t get it all, that’s okay)
So now you have a component with the majority of the solder removed from around its pins. It should be very close from releasing. At this point you want to start at one end of the pins and using your iron with just a touch of fresh solder on the tip, heat the pads while gently pulling on the component from the other side. You get some movement, then you move to the next pin and repeat, then work your way back across. You should be able to slowly rock out the component millimeter by millimeter till it releases.
Be careful about damaging the component you are trying to remove, and don’t pull too hard. You don’t want to pull the pads off the board. Gentle slow progress is what’s needed.
What you should end up with is a removed component and a PCB with a bit of solder on the pads left over. Go back over those pads with new solder and the sucker to clean out the holes. Remove any excess solder from the components pins. Then re do the work with everything going the right way.
Other things that may help: Applying extra flux to the pins/pads. And a product called “Solder Wick” designed for doing solder removal. It’s exactly what it sounds like, a woven metal wick with a flux coating. You press it onto the pin or pad with your iron tip and the solder gets sucked into the wick. This isn’t great for big jobs, but can help with small ones and cleaning up after a lot of removal with the sucker.
Let us know if that helps and if you need some more help or advice with it. And don’t worry about the mistake! Rework is just a fact of soldering, everyone has to do it.