Is it possible, via Google or another search engine, to check whether your trademark already exists?
Yes, but an Internet search does not reveal all existing trademarks. There is no quick way of finding trademarks which are claimed but not yet in use. Your IP advisor can find out from special, dedicated databases whether a trademark is registered or claimed, how long its protection has to run and in which countries or international regions a trademark is registered.
Does it make sense to inquire first from the chamber of commerce about a trademark?
Yes, but again the commercial register can only record those trademarks which are registered, not those which are protected. In fact it is not the chamber of commerce’s role to research whether a trademark is still available.