If your kitchen sink has a sprayer, just spray them off with water. You may have to repeat if you miss any. The soft bodies of aphids are vulnerable to the pressure of even a mild spray.

tj

Ladybugs will not work for you inside your home. Use the water and finger-squishing technique employed by so many of us with great success.

Green Light brand 70% Neem oil will suffocate them very quickly. It's a good organic insect control.

Since a sharp spray of water is very effective spraying the plant with any insecticide is seldom necessary to control Aphids. Since Aphids are most attracted to lush green growth, ie. too much Nitrogen available, it is a good idea to also check the growing conditions of the plant to see if anything needs to be corrected.

Here is a link that might be useful: About Aphids

Continuously spraying your plants with water is a good way to contract a fungus or even start root rot with pepper plants keeping them too wet. You might need to spray with neem twice 5-7 days apart. I do agree that something's not right with the nutrients.

There has been a long standing admonition to not wet a plants leaves because that can encourage some plant diseases to develop. However, recent research has found that spraying your plants leaves can wash off the spores of these plant diseases so they cannot develop into the disease. It is not the getting the leaves wet that is the problem, it is having the leaves not fully dry that is the problem.
Even spraying that sharp stream of water to knock Aphids off a plant daily will not promote plant diseases, as long as the leaves dry in a relatively short time.

And you think spraying them with water is going to help them fully dry??
Moisture on the leaves helps the spores stick to the leaves.

Show me this recent research.