I was like you but I got over it quite quickly.
This is how I did it.
You know that program called Monster Confidence, I think? Where the guy challenges you every day for a month with increasing challenges like Eye Contact --> Asking Strangers for Direction ... increasing the challenge each day.
So I stuck on the Eye Contact thing, being my worst point.
I went out for a walk until I found 100 people who met my eyes. It counted only if I held an eye contact until they passed me or they broke it. I did just 100 because it was winter and not many people were around, and most of those that were, had their heads lowered down. In the summer you could probably go for 200-300.
Do it the whole day if you want to. It's not like you have to walk for 2-3 hours on the dead cold like I had to
I made like 1-2 days pause in between the training days so my mind have time to absorb the new mindset. And did it 4 more times.
After that, my mind wanted more eye contact! It's addictive, seriously!
Now in my everyday activities I actually search for people to look into their eyes...and it didn't take much effort to change.
Just keep doing it and you'll get that snowball rolling into an unstoppable mountain of snow.
Now, a group of 4 bikers passed by me...I kept looking into the eyes of the first one...he broke the eye contact.
Some buff 300 pounds bodybuilder? Looking down.
(I'm mentioning guys just because if you can look those kinds, you can look any woman also)
There is one problem though...while talking to someone, I just can't look anywhere else. I have to wear a string on my finger to remind me to break it, so the person I'm talking to doesn't feel uncomfortable.
Considering looking creepy/horny/weird...my facial expression doesn't change when I look people in their eyes. It's the same as it is right now, while typing this post.
Only recently, when doing it on women, I added a only slightly wider eyes (meaning 10% wider tops, it's subtle but they pick it up...suggesting I'm pleasantly surprised in a way) followed by a sly smile. Gets a lot of smiles back and looks diverted down...even some girls stopped me starting a conversation with "do I know you?"
I think that is all I have to say on this subject. Enjoy!