Is there a solution against nose aches after a lot of swimming?
maybe nose clips, that only let you breathe out and close when you breathe in?
You can buy nose clips on Amazon, a lot of swimmers use them. I don't know what they are like but from what I read some people use them if they have allergies to chemicals in a pool. That could be the problem you are having?
Here is an excerpt from a good article on the pros and cons of using a nose clip.
If your nose is allergic to pool chemicals (e.g. chlorine), a clip might be the solution to keep those chemicals out.
Breathing is less efficient because the nose is shut down and the overall physical efficiency in the water decreases. You have a greater tendency to hold your breath if you wear a nose plug. Holding your breath should be avoided as it is better to exhale continuously in the water because it keeps the body more relaxed and the stroke more fluid. Water might become trapped in the nose and generate snot that can't evacuate. That was the case for me and my nose was regularly obstructed after a swim practice where I had used a clip.
This is an excerpt from an article talks about the reasons why you could have an aching nose after swimming.
Proper breathing during swimming is essential to help reduce nasal congestion and discomfort. If you get water in your nose while swimming, try to continually exhale slowly through your nose. When you raise your head to breathe, do it quickly between strokes. This may feel odd in the beginning, but with practice you will become accustomed to this type of breathing. The pressure of the air that you exhale prevents water from entering your nose.
Both chlorine and bromine are gases in the halogen family of chemicals. Both chemicals are used to sanitize water. Chlorine is less expensive and is often used in public pools. Unlike bromine, chlorine can tolerate sunlight and is most often used in outdoor facilities. Bromine is used for hot tubs and spas because it is easily destroyed by sunlight. Bromine does not have the chemical smell of chlorine, which acts as irritant that can result in nasal congestion. Both chemicals can cause respiratory and skin reactions. They are absorbed through your skin, so showering off as soon as you can after leaving the pool is important.
Inhaled water that lodges in your sinus cavities can cause irritation and infection. This condition is known as sinusitis and nasal congestion is one of the first symptoms. You are more likely to get an infection from ocean or lake water because it is not sanitized and is filled with living organisms. If your nasal congestion is accompanied by headache, body aches and fever, see your health care provider for proper treatment.