I usually find the stethescope is too loud for bearings. I like to use a long stick and hold one end to my ear. It could be you over tightened the tension of the belt. This is a common problem for beginning mechanics. I am not saying you are a beginner but if you are just make sure you did not tighten it too much. I used to do this until I burned out some bearings and someone told be better. Anyway, you should be able to track down where the noise is coming from. Could be the alternator bearing or some other bearing such as the tensioner pulley. As far as remans, they are often lousy, so I try to buy the best I can find even though it is not the cheapest. A cheap one with a warranty is not very good. It just means if this junky one breaks you can take it off and we will give you the next junky one.

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1998 C230 330,000 miles (currently dead of second failed EIS, yours will fail too, turning you into the dealer's personal human cash machine)
1988 F150 144,000 miles (leaks all the colors of the rainbow)
Previous stars: 1981 Brava 210,000 miles, 1978 128 150,000 miles, 1977 B200 Van 175,000 miles, 1972 Vega (great, if rusty, car), 1972 Celica, 1986.5 Supra