As a limb lengthening veteran with a similar starting height, I feel like I am well placed to comment here. I had my operation nearly 2 years ago, started at 169cm (5’6.5) ended at ~176cm (5’9.3).
I think first off here, you have absolutely no idea if it was because of your height. If she didn’t say it was you can’t assume that it was, that’s your insecurity latching onto it. Even if it was to do with your height though, it doesn’t matter. She cares about that, ok, but there are many, many girls who don’t.
I got rejected before and I still get rejected now on tinder dates. I sometimes reject people. Everyone gets rejected, because dating and relationships are very nuanced and we all have different physical and personality features we look for which are also influenced by our environments growing up. Granted I feel like overall I get less rejection (although that could be tied to a confidence thing) but I think for me the important part about getting the operation was knowing that even if I get rejected now, I *know* it’s not because I’m short. It’s something else - even if it’s that I’m not tall (because I’m average.) but that’s what the operation mainly did for me and I don’t regret it one bit.
By all means go for the operation if you have the money, time, and willpower, but it’s not you know absolutely essential to have a fulfilling life - and it’s important to go in with the mindset that this doesn’t magically grant you immunity from rejection, some people will always reject you for one reason or another, because not everyone is a perfect match.
Happy to answer any questions you have!