Yes; following "Christianity" is "the only way to Heaven" and was meant to be defined as "A follower of Christ" (aka GOD) although initially used in a derogatory manner (Acts 11:19-26)!
The "other religions" are our "TEST!" Even though some reside in other parts of the world and have established a "religion" based on their geographical locations, GOD SAID in Matthew 24:14 "And THIS GOSPEL of the kingdom shall be preached in ALL the world for a witness unto ALL nations; and then shall the end come." Why do you think there are so many "Christian" missionaries in ALL parts of the world? READ II Kings 17:29-41! Scripture WILL BE FULFILLED because "GOD does not LIE" (Numbers 23:19)!
"Non-Christian people" can "DO" all they like but GOD SAID "No one can come unto the Father but by [the Holy Spirit] ME" (John 6:44)! GOD doesn't recognize one's "DOINGS!" Romans 8:8 says "Flesh can not please GOD!" Acts 17:23-25 says "For as I passed by, and beheld your devotions, I found an altar with this inscription, TO THE UNKNOWN GOD. Whom therefore ye ignorantly worship, HIM DECLARE I UNTO YOU. GOD that made the world and ALL THINGS therein, seeing HE is Lord of heaven and earth, dwelleth not in temples made with hands; NEITHER IS WORSHIPED WITH MEN'S HANDS, "AS THOUGH HE NEEDED ANY THING," seeing HE giveth to ALL life, and breath, and ALL things." Therefore, what do you think you can "DO" to get "brownie points" to qualify you for heaven?
Consequently, your statement "I strongly believe that the only path to Heaven or hell is through your deeds and faith in God.." is in error according to Scripture! Romans 3:28 says "Therefore we conclude that a man is justified by FAITH [LISTEN!] WITHOUT THE "DEEDS" of THE LAW." Did you hear "FAITH" and not "DEEDS" or "THE LAW?"
READ II Kings 17:29-41 AGAIN!
"Christianity" is NOT A "RELIGION!" I can find NO WHERE in Scripture GOD referred to HIS GOSPEL (Galatians 1:6-9) as "Religion!" Colossians 2:8 says "BEWARE lest any man spoil you through PHILOSOPHY and VAIN DECEIT, after the TRADITION of MEN, after the RUDIMENTS of the WORLD, and NOT AFTER CHRIST!"