I could give you some stupidly patronizing answer like “You just know.”
Or I could say that a big red light starts glowing on your hand like that thing in Logan's Run.
But in real life it's more complicated.
See, in a lot of ways the whole idea of the overwhelming, romance novel love that stops EVERYTHING and has you racing to get a mini van is a MYTH.
Scientists have shown that what we think of as “Love” (where you can't even THINK about another girl, where the very smell of her makes you forget to go to work and where you want to crawl inside her body and bath in her skin . . . you know, the OBSESSION stuff) is almost 100% irrational and chemical.
It's a trick of nature designed to get us to bump uglies and pop out needy little bundles of cute.
And that kind of OVERWHELMING love (which is called limerence) has a built in expiration date like a bottle of milk.
Usually after 3 years or so the “limerence” wears off and you find yourself suddenly realizing that the “perfect girl” you're with is actually not-so-perfect after all.
Only now you've got kids.
And a house.
And this weird scar where your thumb used to be.
That's not to say that “real love” doesn't exist.
It's just to say that it's not as overwhelming and EASY as the movies make it out to
So how do you know if you're “In Love?”
Here's a little shorthand I came up with:
You know you're actually in love with a girl when you find yourself WANTING to be the man she wishes you would be.
Now I'm not saying you'll actually BE that guy (because that guy never looks at dirty stuff online or thinks about other girls, only wants to have sex when SHE wants to have sex and is prone to being CONSPICUOUSLY amorous in front of all her friends even when he'd rather go home.)
But do you find yourself desperately wanting to do whatever you can to make her happy? (Even though you can't “make” anyone happy?)
Do you love having her around?
Do you get as happy about her accomplishments and desires as you do about your own?
Ultimately, as you get a little older and the crazy hormones calm down a bit you'll find out that love is a choice.
And if you want to get out of the dating pool and have the long term relationship thing it ends up being a choice you make every single day.
You wake up, look at the woman in bed next to you and think “I love you” with the kind of passion and concentration of a chess master.
Now, onto the 2nd part of your question:
How do you prove it to her if your past actions have said otherwise?
Consistently. Over time. Every day.
Love is a marathon, not a sprint.