Strong Women Manga

it sounds like LOVE GAME. . .

http://www.mangago.zone/read-manga/dengeki_daisy/ (try the works of this mangaka)
http://www.mangago.zone/read-manga/shiawase_kissa_sanchoume/
http://www.mangago.zone/read-manga/horimiya/
http://www.mangago.zone/read-manga/tonari_no_kaibutsu_kun/
http://www.mangago.zone/read-manga/oresama_teacher/
http://www.mangago.zone/read-manga/ookamidomo_no_shitsukekata/
http://www.mangago.zone/read-manga/beauty_pop/
http://www.mangago.zone/read-manga/kaichou_wa_maid_sama/
also try this list:
http://www.mangago.zone/home/mangalist/963/

http://www.mangago.zone/read-manga/kodomo_no_omocha/ (The girl is very outgoing, confident, and strong. The boy falls in love first and is a bad boy. ;) Of course she changes him.)
http://www.mangago.zone/read-manga/dengeki_daisy/ (Strong female heroine and delinquent male.)
http://www.mangago.zone/read-manga/kimi_wa_petto/ (An independent women looking after a male.)
http://www.mangago.zone/read-manga/koi_dano_ai_dano/

Otomen is good. girl is both strong mentally and physically and the boy although girly tries to be a "man".

Heh, Thanks people! ^_^

Try most of Hwang Mi-ri's works

I'm kinda shocked that no one tried to recommend tokyo crazy paradise yet, but well here are some links all of them are physically strong, mentally, probably.

http://www.mangago.zone/read-manga/tokyo_crazy_paradise/

http://www.mangago.zone/read-manga/basara/

Basara is a real tearjerker in the ending well just a warning.

http://www.mangago.zone/read-manga/saver/

Saver us a manhwa a bit hard to read cause and also a bit confusing

http://www.mangago.zone/read-manga/skip_beat/

Skip beat is more mentally strong rather than physically but she has a special power

http://www.mangago.zone/read-manga/immortal_rain/

Not sure about infatuated guy, but main character is strong i think.

Ooh and I second kitune-san's comment there was this manhwa by hwang mi-ri with a badass main character thats crossdressing as a guy. Most of hwang mi ri's works have strong main characters. So i also suggest her works.

http://www.mangago.zone/read-manga/obaka_chan_koigatariki/