I don't know much about Tylenol 3, except that it contains Codeine as well as Acetaminophen. I believe some doctors prefer you not to take Codeine now.
You can get good pain relief from taking Tylenol, though.
The most effective way to take Tylenol is 2 x 500 mg tablets (Extra strength Tylenol) 6-hourly, to a total of 4,000 mg (4 doses) in 24 hours. You need to take it regularly, to keep up the levels in your bloodstream. If you just take the odd dose now and then, it's far less effective.
Check all other medications you're taking, to make sure there is no Tylenol/Acetaminophen/Paracetamol in them. If there is, scale back one or two of your regular doses, so you stay within that safe 24 hour limit of 4,000 mg.