We also have something called high-cost protection. Not sure if you do. Never heard of it in the US. It means that if you exceed medical or healthcare expenses past X amount, the high-cost protection kicks in and helps pay for it by reducing the prices by a certain %, depending on how much you've had to spend and how long. So you can go from paying full price, to 50%, to 25% to 0%, depending on how much you've had to spend and during what period.
If there's a long period between each purchase or you don't reach the purchase limit, the high-cost protection doesn't kick in. This covers medicine and general healthcare.
That said, I've never had to pay more than a few hundred SEK in medical or healthcare expenses at any one time. Even my 1½ weeks hospitalized only cost me 30 bucks. THat's assuming you do get the treatment you need... Or even get to see a doctor.
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Penicillin allergies must be complete hell. My mother has some allergies to penicillin and antibiotics and I know well how much trouble that's been.