The BIII quota has been abolished and absorbed into the regular high school grade quotas.
Do you know whether you qualified for the BI or the BII quota? I would guess the BII quota but if you were to be considered qualified for the BI quota, it could make a lot of difference.
Assuming that you are competing in the BII quota (with 20.00 + 2.50), you should still have a good chance of admission at most of the Swedish medical schools even if you do not get a high score on the SweSAT (högskoleprovet). Last spring, all of them except for the Karolinska Institute and Uppsala University had admission scores lower than 22.50 in the BII quota (in which case the SweSAT score does not influence your chances of admission through the BII quota).
If you were competing in the BI quota with 22.50, you could possibly be admitted even to the Karolinska Institute regardless of your SweSAT score.
Thanks for your reply! I'm not sure which quota I've qualified for. If I understand the system correctly, I'm guessing I will be evaluated in the BII quota, given that I took some of the required science courses later at university. I assume these would qualify as "kompletteringar" and therefore put me in BII. At least it's good to know there's still hope even if I don't ace the Högskoleprov.
If you do end up getting 1.60 or 1.65, on top of 22.50, you might be admitted even to the Karolinska Institute through the BII quota; the last three spring semesters all ended up at somewhere in the 1.20-1.50 range...