Do you think this is a good way to solve problems in a relationship?

See how long you can go without fighting and bickering and just show affection. When you are no longer able to, talk out whats bothering you, get over it, and get back to just showing affection again. That's a relationship. If the bickering outweighs the happiness, then either take a step back and figure out how to solve the problem, or end the relationship.