'I had' is correct, since the following clause indcates you are no longer worrying, so it has come to an end. If it is an ongoing worry, then 'I have' is correct.

I think "I'd" is more correct, because you are referring to two past events. One is the fact that you were "worrying" and the other is "it turned out fine in the end." Your "worrying" takes place further back into the past and should therefore be introduced with the "past perfect tense" "had." I will also make some other minor corrections to your sentence. "I'd been worrying a lot a lot about some MATTERS lately, but THEY turned out fine in the end" I capitalized the words that I corrected for emphasis only, they don't have to be capitalized. :P I hope this helps!