I would bet that being a new quilter you are making your seams just a teeny bit too big- even 1/16th of an inch will add up and make your block "off". I tend to do that, too, which is fine as long as I am consistent and am the only one making squares for a quilt. When I do something for a swap I try to make a "scant" 1/4" seam. It takes a LOT of practice to get that right. I have been quilting for years and still have trouble with it.
One thing that helps me is to cut the squares just a little bigger and trim the block back to the right size after sewing the pieces together into the block.
Do you have a rotary cutter yet? If you do, what you can do is make all your squares and then find the smallest one and trim the rest to that size. I have done that many many times! I did a drunkard's path (curved seams) quilt recently and squared up every single block after stitching them together. It was my first quilt to come out exactly square and that is after about 18 years of quilting. So don't be hard on yourself- this is supposed to be fun! You didn't spend much on your fabric so it won't be a huge loss if it doesn't turn out exactly perfect. You will still be able to use it and say "I made this!"