What a very cute quilt and you are doing great for a "first quilt". I think you will be able to quilt out the fullness in the block.
For future, when I applique I use a bigger piece then what is called for and then after finish applique I cut it to the size that is called for in the pattern. A stabalizer on and background fabric or starching will help with some of the distortion that is created when you handle the material to do the applique.
All the other advice given is good too. It is a learning process. Don't be too hard on yourself.