Am I right about the meaning?
**Took you like a shot
Thought that I could chase you with the cold evening
Let a couple years water down how I'm feeling about you (feeling about you)**

And every time we talk
Every single word builds up to this moment
And I gotta convince myself I don't want it, even though I do (even though I do)
You could break my heart in two
But when it heals, it beats for you
......

Is this the right meaning of the those marked lines??

(I thought this love was easy and I'll be with you despite the difficulties but it was all pain)

Is "shot" here about drinking?
like she says as easy as drinking a shot (= took you like a shot)

Thanks☺

Question

Am I right about the meaning?
**Took you like a shot
Thought that I could chase you with the cold evening
Let a couple years water down how I'm feeling about you (feeling about you)**

And every time we talk
Every single word builds up to this moment
And I gotta convince myself I don't want it, even though I do (even though I do)
You could break my heart in two
But when it heals, it beats for you
......

Is this the right meaning of the those marked lines??

(I thought this love was easy and I'll be with you despite the difficulties but it was all pain)

Is "shot" here about drinking? 
like she says as easy as drinking a shot (= took you like a shot)

Thanks☺

Answer

Yeah, this whole stanza is a metaphor, comparing the singer's love to alcohol

Took you like a shot /
- probably means, got involved suddenly, and the feelings were intense

Thought I could chase you with a cold evening / 
- generally, after you take a shot, you drink something more pleasant to wash the bad taste out of your mouth (the new drink is called a "chaser" because it "chases" the shot into your stomach). 
This metaphorically might mean that the singer thought they could just leave (into the cold evening air) after they "took a shot" of this person's love

Thought the years would water down how I feel /
- when you "water down" a drink, you add water so that it takes less intense. Here, the singer hopes that time would make their feelings less intense

Answer

yes you understood well
the correct phrase though is "took TO you like a shoot" 
songs would slightly​ change things like they often do.

Answer

It seems pretty good to me, not sure if I understood your question but they look correct to me, that's how I'd say it, maybe change a few words but it'd be unnecessary [emoji]