My inside leg was a similar measurement to yours but I am 5'4". I got a 46cm bike in the end, but I learned that the frame size really depends on the style of bike (road bike, mountain bike, hybrid bike etc all different) so you really need the specific chart for your bike model or similar.
My old bike technically would have fitted me, but I found it very cramped and uncomfortable, and hadn't realised til I had a bigger one what a difference it made.
I am a wobbly cyclist so liked to be able to touch the ground easily, but actually in the end it's more comfortable to have the seat higher and just be able to touch with the balls of my feet, or toes.
There are other things you can change about the comfort too, from how far forward or back the saddle is, how high, how close, and at what angle the handlebars are, and so on.
And it also made a difference to me how big the standover height was. I still find it quite hard to lift my leg over the dropped crossbar to get off, though getting on is OK, and if there'd been a choice for my bike, I might have gone for a slightly lower one.
So lots of measurements that can make a difference. I did buy online in the end, but I measured a lot of things and compared many bikes - if you can find places to try in person, it would be a lot better. I definitely would try not to go too small though - height is not the only important factor.