Your arms look crepey because the skin there has grown thinner and drier, so it crinkles instead of sitting smooth.
Crepey skin is not the same thing as a wrinkle. A wrinkle is a line in one place. Crepey skin is a texture across a whole area, and that difference changes what helps.
It is common, it happens to almost everyone eventually, and it is not something you caused.

Crepey skin is thin, dry skin that crinkles like crepe paper.Arms, the neck and the backs of the hands show it first, because the skin there is thinner to begin with.Sun and dry air are the two things that speed it up most.A thick lotion is mostly water. It sits on top and then evaporates.Daily use is what moves it. Once a week does nothing at all.

The name for it is literal. Crepey skin crinkles the way crepe paper does, in fine lines running in several directions at once rather than one line in one place.

Thin skin that has run short on moisture

Skin holds less water as it gets older. The outer layer thins, the structure underneath loosens, and the surface stops sitting taut.
Press crepey skin gently and it moves more than it used to. That is the giveaway, and it is why crepey skin and a wrinkle are different problems.

What speeds it up

Sun does most of the damage. Years of exposure break down the fibers that keep skin springy. Arms get far more of it than a face that has worn sunscreen since the nineties.

Dry air does the rest. Winter heating, air conditioning and long hot showers all pull moisture out faster than skin replaces it, and crepey skin shows it quickly.

Neither of them happens on a particular day. Crepey skin arrives gradually, which is why it tends to be noticed in a photograph rather than a mirror.

Where It Shows Up First

Crepey skin starts where the skin is thinnest, which is why it is rarely the face that tips you off:
The upper arms, especially the undersideThe neck and the chest The backs of the hands Above the knees and along the shins The inner elbow, where skin folds all day

If you have noticed it in one of those places and nowhere else, that is normal. It does not mean it is spreading.

Most body lotion is mostly water, held together with emulsifiers and thickened until it feels substantial in the jar.

That thickness is not moisture. The water evaporates within minutes and the thickeners stay on the surface. What is left is the greasy film that made you stop using it.

Crepey skin does not need something sitting on top of it. It needs something that goes in and then helps keep what is already there from leaving.

What is in this one

The Just Nutritive Anti-Aging Body Treatment takes the water out entirely. It is seven plant oils and vitamin E, with no water, no fillers and no synthetic fragrance. That is why a small amount covers more than you expect. Hazelnut and apricot kernel are the light ones that absorb quickly. Avocado and kukui nut are the rich ones that stay. Walnut, rice bran and peach kernel sit in between, and vitamin E is the antioxidant. The scent is geranium, grapefruit and lavender oils rather than a fragrance blend. It soaks in rather than sitting on the surface, which is the whole point on crepey skin.

• Three steps, and the third one is where most people go wrong.
• Start with clean, dry skin.Use a generous amount on arms, legs or neck.Massage gently until it soaks in.
• Generous is the word that matters. An oil with no water in it goes further than a lotion. But crepey skin is dry skin, and a cautious amount will not do anything.
• Use it daily. This is the part that decides whether it works. The effect is cumulative, and a bottle used twice a week is a bottle wasted.
• Straight out of the shower is the easiest habit to keep. Skin is still slightly warm, you are already standing there, and crepey skin takes it in better.

Crepey skin responds slowly, so it helps to know what a realistic month looks like.
From the first use, skin feels softer. That is the oil doing the simplest part of its job on crepey skin, and it is immediate.

Across two to three weeks, the softness starts holding all day rather than wearing off by lunchtime. That is the point where most people stop thinking about it and just keep using it.

Between four and six weeks, the texture itself looks smoother. Every skin is different and daily use matters more than the calendar.
Here is what it cannot do. It is a moisturizer, so it softens and smooths the look of crepey skin rather than rebuilding what thinned out underneath. It does not remove stretch marks, it only softens how they read. 

It will not undo sun damage that is already done. And it is not a substitute for sun protection. Covering those arms remains the single most effective thing anyone can do about crepey skin, because the sun caused most of it.