After each oral dose of amoxicillin, peak serum amoxicillin concentrations are reached in 1-2 hours for capsules, film-coated tablets, chewable tablets, or oral suspension in both fasting and non-fasting adults. Elimination is primarily via the kidneys and is rapid, with a relatively short half-life of approximately 1 hour.
What does this mean to you? Well, with most drugs, the first dose starts at a zero plasmalevel, but doesn’t fully go away before the next dose, so the next dose has a “step stool to stand on” and reaches a higher maximum blood level. Typically, it takes 5 or so doses before you approach your ultimate steady-state [i.e. the amount left in the blood by the next dose becomes fairly stable]
With amoxicillin, which is typically taken every 8 hours, all but 1-2% of each dose is excreted by the kidneys before the next dose. That’s why we often precribe it with clavulanic acid (e.g. Augmentin™) to slow down its excretion. Amoxicillin is a sucker punch to the bacterial population in the blood: it peaks fast and hard, but drops relatively rapidly. Fortunately, it has decent antibiotic effects against susceptible species even at fairly low concentrations. How many sucker punches until the enough of the buggers go down to make a difference? You can probably guess that answer is: it depends on how many you had, and how badly they have you on the ropes
However, blood levels don’t tell the whole story. Your body can be seen as divided into compartments, and it takes time for the drug to pass into the other compartments, where they may actually accumulate (unlike the blood, which is constantly filtered by the kidneys). For tissue infections it may take days to reach steady tissue levels; for joint infections, it can take a week or more. The lymphatic system (swollen glands) drain the tissues, so it can take a while, too, despite a near direct boost from the blood with every dose (it can also depend on how well your lympahtics are draining - but that’s something that’s traditionally covered more in DO schools than my own MD training).
Patients usually start feeling better in a day or two. Tell you doctor if you aren’t. Different strains have different sensitivity, and people with repeated exposures to a specific antibiotic (or people infected by them) may have a strain that is more resistant to that antibioltic. Usually even the exact species of the infection is just an educated guess, based on the exam and community prevalence (the quick strep tests are okay, but the definitive tests take days, and who wants to wait that long to begin treating?) Your doctor may revise their estimate, if they hear it’s not working.
You may need a different antibiotic. With amoxicillin, a higher dosage usually isn’t indicated, because the bioavailability (the amount that actually enters the blood) decreases significantly if you go much above the standard adult dose of 500mg. (i.e. if you take 250-500 mg, 74-92% will enter your blood, but if you take 1000mg, you may only absorb 50% so the actual amount entering your blood may not be much higher)