Yes, you can most definitely pray for others, prayer is not only for pastors! If you will notice in the New Testament JESUS himself asked his disciples to pray for Him.
Looking to the Old Testament we see that Job prayed for his friends and God delivered him right after that, Job 42:10. Disciple Timothy states in 1 Timothy 2:1, " First of all, then, I urge that supplications, prayers, intercessions, and thanksgivings be made for all people". Let's look at the book of James 5:16 " Therefore, confess your sins to one another and pray for one another, that you may be healed. The prayer of a righteous person has great power as it is working". Apostle Paul in Ephesians 6:18 says; " praying at all times in the spirit, with all prayer and supplication.
To that end keep alert with all perseverance, making supplication for all the saints". James 5:13 "Is anyone among you suffering, let him pray? Is anyone cheerful? Let him sing praise". These are but a few scriptures paving the way for all saints to pray for themselves and for others. This is the way of a Christian life with our Lord. We are called to intercede for others, nations, peoples and places, governments and the body of Christ. No longer do you have to have a priest receive your prayers for presentation to the Lord.
At the cross when JESUS died the veil in the Temple that separated the Holy of Holies was ripped in two and signifies that our sins now have been paid for and we can in Jesus name approach the Throne of God to make our prayers and expect for Him to hear and by the power of the Holy Spirit grant the grace of healing, deliverance, salvations, and all we need as outlined in the word in the New Testament. We now have the authority as God's sons through JESUS.
See: John 14:13, Romans 8:26, Philippians 4:6, 2 Chronicles 7:14, Luke 18:1, Jeremiah 29:11, Matthew 6:7, 1 Thessalonians 5:17.