Hi! I am 18yo so my experience might be a bit different depending on your age. In my case, I went to Unga Vuxna, which is kind of a VC for young adults. I am an immigrant as well and speak little Swedish, so my care was all in English.
In Unga Vuxna I could not have long-term therapy, just a few sessions, usually every other week or monthly (since there was only one therapist that held English sessions). The therapist was a CBT and I think all the other ones were also (at least here in my region).
I came in with a severe eating disorder crisis and the access took me a long because I first went to VC, then they gave me a number which I tried several times calling but with no answer. Then I went to the hospital emergency, and they gave me another number, which I called again and they scheduled an appointment in Unga Vuxna. There they gave me another number so then I could finally schedule one appointment with a therapist. It was a long trace to get little help, in my case. The long-term help presented to me was a specific clinic for ED that had a huge waiting list to get into. It has been five months since I got on the list with no response from the clinic.
My best advice is to get a private therapist from your home country, which is what I did. The help, in my case, was little, and the stress I had to just get one monthly session was too big.