Just asking from someone else other than Allah is not Shirk otherwise if this were true then we do hundreds and thousands of shirk every day in our day to day life.
Whenever we become ill, we go to the doctor. If we want help, we go to others. If we want knowledge, we go to the one who knows more than us etc…
Shirk is if we believe that besides Allah there is someone else who has the same power like Him. But if we believe that Prophet have power and unlimited power but given by Allah there is nothing bad in it.
The Quran says when Prophet Yaqoob (a.s) became blind after loosing the prophet Yusuf (a.s) and after 35 year when the brothers of Yousuf (a.s) met him in Egypt, he gave his shirt and said rub it on the eyes of my father he will be able to see and the same happened.
So didn't Prophet Yusuf (a.s) ask directly for cure of his father who was also Prophet from Allah (swt). Because he wanted to shows to his brother and other people that they are not ordinary persons but divine leaders and chosen by Allah (swt) and for that it is a must they should have power over everything ( that we call miracle). Therefore it is very good if we ask our needs from Allah (swt) with the Wasila ( means) of Prophets and his Holy Household.
Allah says in the holy Quran:
يَا أَيُّهَا الَّذِينَ آمَنُوا اتَّقُوا اللَّهَ وَابْتَغُوا إِلَيْهِ الْوَسِيلَةَ وَجَاهِدُوا فِي سَبِيلِهِ لَعَلَّكُمْ تُفْلِحُونَ
O YOU who have attained to faith! Remain conscious of God, and seek means to come closer unto Him, and strive hard in His cause, so that you might attain to a happy state.(5:35)