I have been observing aphids on cotton in the fields and getting a lot of calls as well. Generally, we do not have to spray for them, but there are some exceptions to that rule. I have spoken with Extension Entomologist, Phillip Roberts, about this issue. Here are some things to consider and look for: nearly all plants in a field are infested, the aphids are suppressing growth in the upper terminal, the upper terminal is yellowing and leaves curling, there is visible honeydew on the leaves, and/or all life stages of the aphids are present (immatures, adults, winged adults). The decision to spray is a judgement call, but it can be beneficial if the infestation is bad enough. I would be much more concerned with June planted cotton that is anywhere from cotyledon stage to 7-8 true leaves, rather than blooming cotton. We can not afford to hold that cotton back anymore than it already has been.
There are a few treatment options we have. My first choice would be imidacloprid. It is the cheapest choice and Dr. Roberts says you should get about 60% control, which will relieve the stress from the plant and get the job done. The product with the best efficacy is Assail, followed by Centric, but both of these products will be more expensive.