Hi Dizzy! What you are seeing is probably the result of the anti-aliasing around the original image. (But then, you probably already knew that.)
There are a couple of ways to make it "go away," that don't include the use of another expensive plug-in.
Since you are working directly in the Alpha channel, simply blurring the Alpha might do it, as it would give you partial transparency in the problem areas. But, since that transparency will be placed on white when you import to SL, that's not going to work unless your image is very, very light in the first place.
If I were you, I'd extract the image first, and put it on a transparent background. That will allow you to use the special PS tools that are there to manage this kind of problem, and also allow you to match the colors on a layer beneath the image, which will eliminate the white halo in SL.
Extracting the image is fairly simple.
First, if it's on a locked
Background layer, you need to get it on a normal layer. You can do that by just double clicking on the layer, and clicking OK in the dialog that opens. (Or if you want to skip the dialog, hold down Option/alt when you double click.)
Or you can make a copy of the background on the layer above by simply tapping Command/ctrl J, and work on that layer.
Once you've done that...
If your version of PS has the Extract Filter, you can use that. It's very good about making semi-transparent pixels on the edges of things. (Let me know if you need a short tut about how to use the thing.)
Or, you can make your selection as you normally would, and then use the Defringing tools to get the red out.

You'll find them at the bottom of the Layer menu, under Matting.
Or, since your selection is on a solid color background, you can use the Magic Wand to select it, then go to Select > Expand and expand it by one pixel. Hold down Option/alt and click the background again, to subtract the background from the selection. That will leave a 1 pixel selection that surrounds your image. (There are a few other ways to do that, but I've found this method to be the fastest, for me anyway. Feel free to try a different one.)
Then, go to Edit > Fill, choose 50% opacity, and Clear as your Blending Mode. (If Clear is dimmed, you forgot to make the Background into a layer. Also, it doesn't matter what is in the Fill portion, since it's not really going to be used.) That will reduce the opacity of that single pixel outline to 50%, which might be enough to make the red unnoticable, especially if you place another layer under it, for those semi-transparent pixels to "pick up" when brought into SL.
However you do it, when you are ready to make the Alpha, just hold down Command/ctrl, click on the thumbnail image of that layer in the layer palette, and Save Selection. If there's already an Alpha, Replace it; otherwise make a New one. (Remember, there can be only one.)
Hope this helps!