From Islamic knowledge we know this about Aqeeq...
The benefit of Aqeeq is that it creates joy in the heart, is good for eyesight and it helps illuminate sadness and anger. It is also revered in other religious and has been in use from the time of Hazrat Adam ( a.s.). It absorbs the rays of the sun and passes these onto the body and is good for health. Black Aqeeq protects children from envious eyes.
Modern knowledge adds to that some more practical benefits of aqeeq in everyday life...
Among the New Age community, believers revere Carnelian's mental grounding power and believe this is the source of its greatest mental effects. They say it teaches one to focus on the present for the moments in life when all one's mental powers are necessary for success at a single, important task and is a source of confidence, eloquence and inspiration. For instances when you need a boost to creativity for problem-solving, Carnelian can assist in getting the mind out of mental ruts and back on track for success. In the long-term, it bolsters ambition and drive and reminds the wearer of the future's goals, hence becoming a powerful tool in major decision-making. Overall, many hold Carnelian dear as a stone with the ability to protect the individual, bolster confidence and generally enhance and expand the experiences of life.
Agate deeply nourishes your physical body with earthtone color rays while fostering cooperation among all of your body's parts. By opening lines of communication within your body, Agate's earthtones help coordinate your body's myriad functions. Agate also alerts your body's innate intelligence to your current state of health so that your body can rally its own resources to resolve any disharmonies. By flooding you with life-giving earthtones, Agate helps you forge a stronger connection with the Earth and feel more grounded and comfortable living in the physical world. 
More about its effects
Carnelian stimulates, sharpens, and enhances mental functions. It improves mental clarity, memory, and the ability to see things from a higher viewpoint. When you first wear Carnelian, it stirs up the clouds that inhibit mental clarity. Consequently, you may notice that your clarity seems to decrease, and your sinuses and lymph glands may become somewhat clogged. This effect won't last long. Carnelian teaches the body to metabolize these clouds. As more and more clouds are metabolized and eliminated, your clarity will increase and surpass what you experienced before putting on the Carnelian. You will also gain the strength to help you accept the many changes this increased mental clarity will initiate in your life.
How to choose a good quality stone
Carnelian's quality is easy to judge with the naked eye. A microscope is not necessary and a light table may even be deceiving. With Carnelian, color is more important than clarity. Nonetheless, to be therapeutic, Carnelian must be free of any rock matrix or non-Carnelian inclusions. The Carnelian should not appear muddy or dull. Cracks, even small ones, should be avoided, because they disrupt the Carnelian frequency.
The color of a Carnelian sphere as it is visible to the naked eye in sunlight is a true representation of the energy it will give to its wearer. To see Carnelian's true color, it must be held up in the sunshine outdoors, though not directly in front of the sun. In this respect, Carnelian is different from some other gemstones: any light source placed directly behind Carnelian makes it appear lighter than it really is. Carnelian color should be as consistent as possible throughout the sphere and, ideally, true to the pure orange seen in a rainbow. Such Carnelian is not plentiful. For many people, this optimal Carnelian color may actually provide too strong an influx of orange ray. Therefore, in most cases, using the Carnelian with a slight hint of red coloring is recommended; it emanates a degree of orange ray that is in balance for most people. The more commonly available, dark red-orange Carnelian is not therapeutic.
Well-formed spheres are vital to Carnelian's effectiveness. Irregularly shaped spheres diminish the strength with which it can express its frequency into the aura.