Welcome to the forum.
Yes, you will need to have your qualifications recognised by the Swiss Red Cross.
Swiss Red Cross (SRC)
3084 Wabern
+41 58 400 44 84 (Mo-Fr, 08.00am-12.00am)
www.redcross.ch
And yes, you will have to prove you speak a Swiss language, probably at B2 level minimum, but they will be able to confirm what level you need.
Be prepared, this may be a long process. Iirc it's taken some nurses 2 years to get recognised to be able to work here.