I'm one of those Asian guys who spent his middle+high school years in an all-boys school with barely any contact with women.

I'm 19 now and I'm still a virgin (it's pretty normal in my country) and holding hands with a woman that I'm into still gives me a hard on.

Is this normal and does it go away with experience, or should I practice meditation?

Asian guys are always introverted, that's bad mate, i bet you are also one of those.
Where do you live?

If she holds your hand it means that she likes you.
Grab her by the 2 hands and look her in the eyes, see how she reacts, if she blushes then hug her.
Go from there.

Since you are holding hands for quite long time, you have to slowly slowly escalate, give her time.

I also bet she's asian too, so she might be shy as well so she needs more comfort (in this case comfort = time)
Best of luck

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Gotta put da cream!

I live in the us but I have a lot of Asian friends. They are incredibly shy and prudish. Lots of slow escalation and don't be too afraid of your erection. Just don't touch her with your dick. It will go away with more ejaculations.

I recently learnt about green, yellow and red girls. Green girls give obvious IOIs (indicators of interest), yellow girls give IOIs but they step back in order to not seem slutty but soon they are sending more IOIs driving AFCs crazy and finally there are red girls. These are the girls that do not give IOIs but secretly want it. The reason this is relevant to you, particularly if you are dealing with Asian American girls, is that a lot of them are red girls. They were raised culturally by their parents not to express their IOIs. (Common with Catholic girls who did not rebel as well). The point is you should look into frames. Future (Master PUA) does a killer summary of positive frames in Love systems 11 essentials (you can torrent it for free at Torrentz). It says that you have to over power a red girls frame in order to get anywhere. Last night a yellow to red girl was saying good night to me at her door. I was getting no IOIs. I so I pulled the fake walk away. She closed the door. I thought it was over but then I remembered frames. I turned around, knocked on her door and kissed her hard before she could get a word out. If you are uncomfortable with the sudden kiss drop the line from Cajun's webdating seminar "I am the type of guy to make the first move whether it is a romantic kiss good night on the door step or throwing you up against the wall and making out with you hard in the rain". Her reaction to the second line will tell you everything then kiss her. There is no way I would have done that in the past but because of that I got to rock her world all night long.