2001 Toyota Corolla Started making noise after oil change

Noises problem
2001 Toyota Corolla Front Wheel Drive Manual 72,450 miles

My car starting making a noise following an oil change five months ago (I have had my oil changed twice since then, once by the same place, the second at a different place). The noise starts when I get up to higher speeds (above 45/50). The only way I can discribe the noise is it sounds like a diesel vehichle (which mine is not). The engine light has not come on. When I took it back to the original garage and told them what noise it was making, he drove it and told me a gear was out and I needed a new transmission (I have a 5-speed and it shifts smoothly) and it would cost me $1600 plus labor and if they needed to replace the clutch that would be extra (clutch seems strong to me). I took it to the 2nd garage and asked them to verify. They said it needed a new transmission and that would be from $2500 - $3,000. I have since talked on the phone to a Toyota mechanic that told me that whoever changed my oil must have bent the heat shield and caused it to vibrate. The Toyota mechanic also said if it was the transmission, the Check Engine Light would be on. Please help! I don't have thousands of dollars to fix.