Big toe swollen, slightly painful & red at both sides of the toenail?

Painful toe: Likely gout but could be cellulitis. Needs evaluation.

Poorly cut toenails: If one does not cut the nail straight at the edge or with a slight curve, it will get red and inflammed, which usually means the cut went low and into the cuticle. That area is also the most common to get an acute gouty episode, but this is usually one foot and mostly very painful.

Abscess: Abscess caused by ingrown nail.

Infection: Nail borders have broken the skin causing bacteria to develop in the area.

Ingrown toenail: Sounds like an ingrown toenail. But to be safe, and for treatment, i would suggest checking in with a specialist.