Don't give up hope - I am a 33 yr old 5'10" Asian American male and I am dating a redhair/blue eyed 5'10" able to wear bikini bombshell 26yr old girl who makes more money than I do(she has a masters in Chem Eng), I make 70K(which is not pocket change) and she blows me out of the water.
I guarantee I have a bigger head than you as I am filipino and filipinos usually have big heads - and my head is bigger than most filipinos. Let me add that I'm also kind of chunky and not particularly good looking. The penis thing - go for decent girls -you can find them in Church, but they are everywhere you just have to look. I guess thats one reason the Catholic church says no to premarital sex.
Whats my secret - finished school and developed myself personally. First off start eating more meat. The extra hemoglobin in your blood will make you more passionate. When I was fasting from meat during lent(as a filipino catholic) - I noticed that I became very luke warm and not much drive. Filipinos are also known for being the most passionate lovers in Asia - again this is because we eat so much meat. Most other filipino guys I know are dating latinas(and we know how passionate latinas are-they also eat a lot of meat). Eating meat along with liting will help you get a bigger build. Also go for girls your height or shorter - its not an asian/white thing it has to do with girls just don't go out with shorter guys which cuts across races.
Back to school - at first I went into computer science then noticed ppl weren't getting jobs so I switched to accounting. While you are in school I can assure you it will be tough to get girls. Heck I had ZERO girls in college. Its okay, just concentrate on your studies. See you will do well being an engineer as the engineer job market blows other undergrad degrees out of the water. Having a good degree will set you apart later on in life. Don't buy a honda accord when you graduate - get a sports car like a Z. Trust me - girls don't like broke a_s guys. When you get my age you will notice that being a professional puts you in a higher class. Just don't talk about engineering, anime, computers, or other dorky stuff on dates. If they do ask keep it at a minimum and use discretion(ie talk all you want if they love anime). You interrogate them and I mean let them reveal the map so you can have a strategy.
I would add that you need to join more clubs to enhance your career and learn how to use english better(join toast masters) than white people. As an auditor - I have learned that english is a very powerful tool which can take down much bigger people than me(my auditees). Talking to girls I have learned how to be charming(through my use of language) and learned how to listen to them(super important). Learn how to be charming - ask and observe how non-goodlooking guys who get beautiful girls operate.
Learn your culture - girls go for exotic. I have filipino cd's in the car - I used Imeem to find out what I like. Asian R&B(in my case filipino) will melt their hearts. Teach them your language - if you don't know your own language - I suggest going to Amazon and buying books - they go crazy when you call them sweetheart in a different language. Learn how to cook for your culture and different cultures. Chances are the girl won't know how to cook - I am able to use this knowledge strategically to put in the girls head why "I don't need her." This is important as she will seek your acceptance.
Don't be too nice to girls for no good reason. The reason is you don't want to be put in the "friends bucket", but you want to be put in the "possible mates bucket." So learn how to talk - For me I grew up in a rural area so it not a problem for me as I can control my "ballsy-ness" (aka showing of testosterone) which you need to show at times. My personal favorite is going to starbucks with friends and telling all my male friends to go buy their "wussy drinks" while potential female are around. Then you just explain to the woman that your not very P.C. - it shows that you don't care what lesser people think what you should do - just don't go overboard.
Learn how to dress - ask a girl or female cousin to dress you. Gay guys can help you the best in the styling department - so don't be homophobe and use that resource. Know what colors go good with your skin. I always have nice shoes. Have a good wardrobe once you get a professional job. I have French cuffs with jeweled cuff links, cowboy hats with big kicker belt buckels and boots, tuxedos, chinese style outfits, and nice suits. While you are in school - just spend your money paying for tuition.
On the personality end - don't be cheap but don't go overboard(ie don't take a girl to the most expensive restraunt in town). You got to build up. Learn how to flirt-start with waitresses- they know the more they flirt the bigger their tip-its a very good training ground. Flirt with all types of girls not just the super hot ones - heck black girls can teach you alot in this department. Always be charming and not wussy or needy.
On society - stop watching tv and playing video games. American media fills peoples minds on how weak Asian males are - which is a lie you shouldn't believe. I myself don't have a TV. I go to lots of social events and places around town. I do watch though tv programs from the Philippines off the internet - Its nice to see people who like me in media - and I have learned alot of my culture.
So my main point is spend your money now on school. After school become a cool dude -because you have the money and the education to justify it. Being a professional will set you apart.
If you need more advice just let me know...