Is it normal that my stubborn fat feels "lumpy"?

I've been trying to lose weight for about a month now and it's been going pretty well. The areas where I have fat the most are in my upper arms (which are drooping, unfortunately) and my inner thighs. I have a knack for "feeling" my fat to keep me motivated so that I know how much fat is on my body and how much work I have to do to get rid of it (I sound crazy hahahaha). I was pinching my arm fat and moved the skin between my fingers around and I felt some tiny lumps inside, kind of like little of fat under the skin. They are painless of course, however the entire area feels clumpy. Is it normal that fat feels like that? Or is fat suppose to feel "smooth" under the skin? Can I completely get rid of those fat clusters with good nutrition and exercise?