It will probably be a gradual response, depending on how damaged your intestines were to begin with. But it definitely will not hurt to take a vitamin supplement, and in a few months have your doctor do some blood tests to check vitamin levels. My iron was low for no known reason for a long time, even though I took an iron supplement daily. 5 months after going gluten-free after my celiac diagnosis, my iron levels are normal. I didn't have it tested in between those 5 months so I don't know how long it took for it to get back to normal.
Since you are in a different country than the US, I would start by seeing what brands of multivitamins are easily available at your local stores, and contacting the brands to see if they are gluten-free. That way you don't have to pay a lot by mail order.
I am my husband's "Silly Yak Girl"
I was diagnosed with Celiac Disease in January 2013. I also have Lupus and Common Variable Immunodeficiency(CVID) for which I am on IVIG.
Celiac.com - Celiac Disease Board Moderator