Both are really common in my area (due to the near constant rain 8 months of the year!)
Most abscesses aren't a big deal- the horse typically presents as 3-legged lame seemingly out of nowhere, and for the first time seeing it, many people think the horse has broken his leg
Soaking in epsom salts and applying an epsom salt poultice daily helps to draw out the infection (as well as keeping the horse's feet as clean and dry as possible), continuing for a few days afterwards as well. But if it hasn't burst within 2-3 days calling a vet or farrier is in order, and they may dig it out. When the abscess drains, the relief is instant. Sometimes the abscess will come out badly, or partially drain, get plugged up, and then reoccur, or the vet/farrier will have to remove a lot of material to find the abscess. This will mean that the horse will have a longer recovery time, sometimes months. It sounds it came out badly when it burst, taking some of the frog with it. I'd consult your vet as to how long you should expect him to be so sore, and when you should have a follow up if he's not better, but you can probably alleviate the pain a little bit in the mean time by getting some hoof boots for him (it sounds like he's probably barefoot?)
For mild thrush, using iodine for a few days should clear it up unless there's an outside factor encouraging its growth, such as deep sulci, contracted heels, constant exposure to moisture, etc. If it hasn't cleared up in a week or so of treatment, consider if anything in his environment is contributing to it.