My toe is red, swollen and painful around the nail but i think it's from trauma, can i still have an infection and what to do?

Trauma/infection: Trauma can certainly cause the symptoms you describe. You can also get a secondary infection from the damaged skin where the trauma occurred. The damage from trauma will normally get better if you put ice on it. It also will gradually improve and won't get worse. If the redness, swelling, or pain worsens or doesn't resolve, you need to see a doctor as you may have a secondary infection.

Paronychia: Paronychia is a skin infection that occurs around the nails. Paronychia is fairly common. It is usually caused by injury to the area -- for example, from biting off or picking a hangnail or from trimming or pushing back the cuticle. Bacterial paronychia is caused by bacteria. Candidal paronychia is caused by a specific type of yeast. Fungal paronychia is caused by a fungus. Both can occur at once.