It is more natural to make trouble singular. The the two sentence do not have exactly same meaning although they are similar. "I got into financial trouble" is nonspecific - it may not have been your fault. "I got myself into financial trouble" - you are saying it was your fault.

Well the second one is more natural. Actually, In the fist example; “I got into financial troubles.” sounds awkward as a plural. It would be better to say; I got myself into financial trouble.