As the spouse of a Swedish citizen,

> You are entitled to receive a residence permit if you are married to,
> have entered into a registered partnership with, or are the cohabiting
> partner of someone who lives in Sweden. Your partner should register
> your marriage or partnership with the Swedish Tax Agency.

[Source][1].  However, [the process to get this permit][2] sounds rather complicated and painful, I would advice getting started on it ASAP.

The following page claims also you're entitled to a free visa and expedited processing if the purpose of your travel is to join your spouse:

https://europa.eu/youreurope/citizens/travel/entry-exit/non-eu-family/index_en.htm

...but this may be incorrect (despite being the official europa.eu page!), so let's wait for @phoog to get back to us.


  [1]: https://www.migrationsverket.se/English/Private-individuals/Moving-to-someone-in-Sweden/Spouse-registered-partner-or-cohabiting-partner.html
  [2]: https://www.migrationsverket.se/English/Private-individuals/Moving-to-someone-in-Sweden/Spouse-registered-partner-or-cohabiting-partner/How-to-apply.html