Is it normal/okay to fall in love with someone after a few minutes/hours?

This is how I met my first big love. I saw her once at a college party. I instantly felt that she was the one and I had to do everything to be her man. We talked all evening, we had a connection and everything was going great. She told me her facebook, but because I was a dumb, tipsy cock I didn't write it down, thinking I'd remember it. We had fun, but she had to leave early, cause she had an exam or a project... Then I proceeded to get wasted with my friends, telling them about said amazing girl, still not writing down her facebook.
Next day, I couldn't remember her facebook. I was furious and hated myself. Decided to go for a drive to feel better and then I saw her in a bus going the opposite way. Hit the gas, did an illegal U-turn and chased down the bus. Halted the bus, barged in and got her details and took her out on a date. Such luck don't come out of nowhere.
We were together for 2-2.5 years and life was a dream. Then her parents moved to the US and sadly she had to go with them... I'll always remember that intense feeling I got when I saw her in that bus. I hadn't lost her. Heck, if I had a better job then and made more money, I would have married her! But life goes on. One door closes, another one opens.

There's a difference between fancying somebody and falling in love. Unless you're like stalking these people after an exchange of pleasantries in the supermarket, I'd say normal.
*edit I read your other comment and have gone with not normal.

Well of course, it’s called “Love at first sight” if you’ve never heard of it.

what you felt is lust, not love. And it's not okay. that's how stalkers are born. Try to get to know someone first.

Please don't go and kill the person when they try to break it.

Everyone falls in LUST often. Love that's a different story.

I tend to think of that sort of thing as a crush or infatuation, but not as love.

You're probably getting aroused. Not sure whether it's love. But yeah it's all good

it helps if they just got you off in a sexual way