It's completely normal for a penis to curve one way or another. Most curve slightly upwards but some curve left, right or down. In extreme circumstances, with curvature in the 45 degree range, they can correct this with surgery if necessary but the correction method requires shortening(!) the penis. No, it's not something to be embarassed about, relax. During sex, if your curvature ever causes your girl discomfort, you can try a few different positions and find the one that works for you two.
My penis curves to my left probably 20-25 degrees. I used to worry about it, but I've gotten compliments on it, so as I have gotten older and more self-accepting and have seen other men's penises, I now know it is very normal and have come to appreciate the uniqueness of it.
There is something named "Peyronnies" disease. The penis doesn't do a soft curve, it takes a right angle (in my case upwards), there's a hard spot where it curves, and with time the curve actually moves up and down the shaft. The curve started at the tip of my penis and then traveled up, then went down again. Now it's in the middle. When limp or hard--it looks broken. I've had this for 8 years, surgery is the only answer, as I can still function, I'll live with it. There was a period of 2 years where I couldn't function though, but with time it has softened a bit. It's an autoimmune disease. My body rejects my penis ~ talk about stupid!!