I have a problem: I get an erection at the drop of a hat. I'm 21 years old and not some overactive adolescent. I am not sexually active and will not be until marriage. I am dating a girl right now and if there is the slightest physical contact between us I get an erection. If she even says something sweet to me I get an erection. I am not thinking about sex or anything like that. Needless to say, if we are sitting and holding hands or cuddling a little bit, I have an erection for long periods of time. This has been embarrassing several times. I cannot wear a tucked-in shirt around her as my erection is then very visible. This has been embarrassing, but the worst part is this: there is a clear liquid that drips from my penis when I have an erection. After sitting and talking for a couple hours and, of course, having an erection that whole time, I will have a wet spot in my boxers so big that it leaks through even jeans, leaving a visible wet spot on my jeans. This is very embarrassing! Fortunately, she hasn't noticed it yet. I don't know what to do or if I can do anything. The wet spots through my pants are terrible.
Your problem is not at all unusual. I have wondered on more than one occasion if the popularity of baggy pants and untucked shirts among teenage boys is driven, in part, because of erections and spotting.
Even though you have passed your teenage years, it doesn't mean that you have finished development and all the adjustment problems that come along with it. The average boy reaches his adult size generally between the ages of 18 and 20, though a young man may still grow a half an inch or so in his very early twenties. However, the male brain doesn't complete its changes until age 24. (That is why insurance rates for men remain high until then.)
You don't have to be consciously thinking about sex to experience arousal. Strong feelings for another person can trigger sexual arousal. You didn't mention this, but I suspect that you are seriously considering marrying this particular young woman. Love is developing and your body is naturally responding to your attraction to this woman.
Along with your erections, you are producing lubricating liquids from your Cowpar's glands (what is commonly called pre-cum in slang terms). Just a men differ in height, weight, and strength, men differ in the quantities of liquid produced during arousal. Some produce very little, no matter how much they are aroused. But others, such as yourself, produce significant amounts that can leak through clothing. By the way, men can and do generate liquid independent of having an erection. As you get a little bit older, you will slowly gain some ability to control your erections by conscious thought; however, I don't know of anyone who has been able to control their Cowpar's glands.
Given that it is a fact of adulthood life, there isn't much you can do about it. It is much like wishing that your nose would stop running when you have a cold -- it is not going to do it just to please you. As you become more comfortable being with this woman, your body will slow down its dramatic reactions, though it won't completely end. But, of course, you want to know what to do in the meantime.
The only practical suggestion I can offer besides what you are already doing, is to get some napkins or paper towels to carry in your pocket. When you know you are about to be in a situation that is going to cause your body to overreact, excuse yourself and head to a restroom. Put a folded napkin over the end of your penis like a tent. This will help absorb much of the liquid. Just remember to change it periodically. Eventually the liquid is going to soak through if you don't. Keeping a spare set of undershorts and pants in your car to change into if your pants get soaked wouldn't be a bad idea.
As far as the erections go, position your penis such that your erect penis will either go down one pant leg or straight up your front. At least then it won't cause your pants to noticeably bulge or make you uncomfortable. Pants made of heavier material, such as jeans, won't show erections as much as lighter weight pants, such as dress pants. Keep in mind that you notice the erection more because you can feel it than someone else will notice.
If your girlfriend does happen to notice, try to be casual about it without getting graphic about your problem. Something on the line of "Yeah, my body keeps overreacting when I'm near you. It can be embarrassing." Believe me, girls have their own set of embarrassing body functions, so she will likely be sympathetic.