Your grammar was wrong initially, you should have used 'grew' not 'grown'. But the sentences 'I was born in and grew up in Salvador' or 'I was born and raised in Salvador' are both fine. I suppose which one you use is up to you. I would usually go for 'I was born in and grew up in...' unless I was making a joke about my heritage to my friends and would usually say 'I was born and raised in...' in a mocking tone. Perhaps 'I was born and raised' is American English?

If you want to talk about being born and growing up in a place and you would like it to be simple you would write: I was born and raised in Salvador. The reason for that is if you wrote: "I was born and grew up in Salvador" it doesn't sound quite right for some reason. It would have to be written longer: I was born in Salvador and I grew up there as well. -->this is too long, unless of course you prefer to write the longer way. But if you want to say it right to the point then "I was born and raised in Salvador" would be used.