I've had a couple of guy friends who have worried about the same thing so I'll address the obvious in the 3rd paragraph. (And my father who's 5' 4 1/2" and has been miserable his whole life over it. But he's from a much different generation…)
I gained almost an inch in height (at age 33) after back surgery. Simply because I improved my posture through physical therapy and adopting the sitting and standing poses that would cause me the least pain. I didn't have bad posture in the least before I had to deal with my back injury, but you can gain a lot of height simply by doing yoga, strengthening your core and your back muscles and concentrating on how you're carrying yourself. I found my shoulders and upper back to get much stronger and more defined during my long process of physical rehab, and maybe the definition of my upper body makes me look taller.
But, most important point, some men are very uncomfortable about being shorter than their girlfriends but nothing is going to change that. You just have to accept it, carry yourself well, and forget about it and be self-confident. Your improved confidence will make people perceive you and your GF as a perfectly matched couple. It's just stupid and self-defeating to worry about something you can't change. And the way you carry yourself is the way people perceive you.
btw one of my best friends is beautiful, blond and 6 feet tall. This has not been easy for her. Now she's happily married for 5 years and has a child with someone who's 5' 9". She loves him, their baby is amazingly handsome and all is well.
No one has it easy. You have to deal with the cards you were dealt. Stop tripping about it and things will improve. It is what it is.