I do all my quilting on a regular sewing machine. There is no requirement to get a long arm. Free motion quilting just means you guide the fabric, not the feed dogs (either by lowering them, covering them, or just ignoring their resistance with a foot that doesn't have much pressure). It has nothing to do with the machine. Almost every sewing machine is capable of free motion.
If you feel your quilt doesn't look like most quilts, it is likely because the quilting you did doesn't match current style. You say you did squiggly lines on the seams. I know, personally, that I see most quilting either inside blocks or all over the quilt. By focusing it on the seams, you just chose another style. It won't look like quilts of another style. It likely still looks very nice though.
I also agree though- quilt as you go does generally have a different look than a quilt that is done in one piece. Just a different look though, not better or worse.