Okay, I finally managed to get rid of all the black lines. As JA12 & MadeWithFeet suggested, I had to paint further outside the lines of UV Map to get rid of the lines. However, instead of using Texture Bleeding which was giving me rather limited results, I decided to paint directly onto the texture map in the UV Editor.
Once I was finished, the UV Map ended up looking rather messy for my liking but the end result is that there is no longer any visible black lines on the model, so I guess I’ll just live with the messy UV Map if it works.
I mean its not like I have any other alternatives, I tried looking into other freeware programs for texturing 3D objects and I couldn’t find anything, so I guess I’ll have to stick with Blender for texturing with Gimp 2.0 to help out.
Anyways, unless anyone else has anything to contribute to this forum topic, I guess I’m done with particular subject & I’ll close out by saying thanks to everyone who contributed!