I attend high school in Chicago. Everyday I miss two prayers, Zuhr and Asr. Which one should I pray first at Asr time?

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
No doubt that the prayer is the second pillar of Islam and it is the most important and greatest form of worship for Allah. So, it has a special importance in the life of the Muslim as it brings happiness in This Life and The Hereafter. So, one must be sure to perform it with all its obligations, Sunan and supererogatory acts. Allah Says (interpretation of meaning): {but when you are free from danger, perform As-Salât (Iqâmat­as­ Salât). Verily, the prayer is enjoined on the believers at fixed hours.}[4:103]. Allah also says: {Guard strictly (five obligatory) As­Salawât (the prayers) especially the middle Salât (i.e. the best prayer ­ 'Asr). And stand before Allâh with obedience [and do not speak to others during the Salât (prayers)].}[2:238].
The Prophet once mentioned the prayer and said: "Whoever takes care of it, it will be a light, an evidence and a safety for him on The Last Day. And whoever neglects it, he will not have any light nor evidence or safety on That Day. He will be resurrected on The Day of Judgement with Qaroun, Pharaon(Pharaoh), Haman and Ubay Ibn Khalaf", [Imam Ahmad and Darumy]
There are many more sound texts in Qur'an and Sunnah that emphasize the importance of prayer. So, we advise you to preserve your prayers and perform them in their fixed times.
Nothing should occupy you from doing your prayer as prescribed by Allah The Almighty. Know that anything that you prioritize over the prayer, Allah will not put any good in it.
As for your question, you should pray Dhuhr in its fixed time and the reason you put forward is not enough. Know that delaying it from its time, without a dire necessity, is a grave sin. So, we do not believe that you should delay Dhuhr to the time of Al Asr.
You can pray Dhuhr during the breaks between sessions and if you can pray it in congregation with other Muslim colleagues that would be more perfect and if you can not do that, pray Dhuhr in any pure place at your school as Allah The Almighty, from His Kindness, has made the earth a mosque and a pure place for us to pray. So, the person should pray the obligatory prayers in their fixed hours anytime the prayer is due.
Know also, dear brother, that your praying in those places and your showing your pride to be Muslim as well as your having a distinguished Muslim personality by being in relation with your Lord all the time and everywhere you go, all these things have a great impact on the people's hearts. This in turn will let these people admire you. The Muslims who have weak personalities and who apply Islam timidly do not get this admiration.
As for your question regarding which prayer should we pray first when Dhuhr is delayed to the time of 'Asr, the answer is that Dhuhr must be prayed first.
Allah knows best.