That decision is up to you. If this was me, would I reach out? Absolutely. However I would not be asking for forgiveness. Instead I would say something in a direct matter-of-fact way such as “I may have taken a wrong turn.”
Most forum members here will reply in a ‘paint by numbers’ or , ‘one-size-fits-all’ type response. In many cases this is not only lazy advice, but it will backfire.
While it is true that we should be the “prize” that women have to earn, We also need to be self-objective.
Personally I agree with you about Valentine’s Day. I think it lacks soul, is commercialized, and men are typically intimidated into doing something, instead of being inspired to do something.
Women typically see this as something entirely different. A lot of times it’s not about you, But also about them seeing their friends get gifts and then filling inadequate or undervalued.
Your girl, did not receive a gift, and also saw you give a gift to another girl. No matter your intent, women are emotional and she’s made a conclusion.
With the above observation, do you think she’s going to view you as a prize that needs to be earned? Likely not.
Although you do not want to gravel or ask for forgiveness, a handwritten note stating that you can understand how this misunderstanding could make her feel … and that you’d like to make it up by buying her a cup of coffee a meal or whatever you think is appropriate, will (I believe) work much better in your favor.
My advice does not come with 100% guarantee. But I do arrive with a lot of past experience with women; Which also includes a lot of my very own “cleanup on Isle three.”