I think this sentence means:
"Now that you mention it, I am feeling good."
Is this right?
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To break it down...
言われてみれば -- now that you mention it
そうだった -- it was so ; that's right ; you're right
気もし～ ← 気がする+も -- I feel~, I think~, I feel like, I have a feeling that~
も -- (particle to make the statement sound softer/milder/reserved.*)
～てきた -- have started to~ ; I'm beginning to~
な -- (sentence ending particle)
"Now that you mention it, I'm beginning to feel like it was so."
* For more on this usage of も, see: What is the difference between 「とは限らない」and 「とも限らない」 / Usage of も in a Specific Context / も in 「Vのもアレなんだけど」
I can see why you might think that, but that would be 気持ちいいな。or something similar.
Your understanding of the meaning of 言われてみれば is good. "Now that you mention it"
そうだった is "that was so" or "that's the way it was"
気もしてきた is basically "I have come/begun/started to feel the same way, too"
So now you ought to be able to put the pieces together and re-translate it on your own, I think. ;)