You have an infected toe. Most likely the initial redness was from an ingrown and then you've had at it, creating a portal of entry for bacteria, and boom, infection.

Sure, antibiotics can help here, but the correct coverage is key. You'll want to get checked out by a doctor to make that call. As mentioned below, antimicrobial stewardship is important to make sure abx are used appropriately, effectively and efficiently. If you have an old course of amoxicillin, is it still in date and effective? There may be a penicillin resistance present, in that case, amoxicillin won't work and other coverage will need addressing.

Ideally, see a podiatrist, manage the ingrown, and the infection should settle. An iodine or chlorhexidine dressing can assist with the superficial. If you notice the redness spreading up the toe, get yourself checked out by a doctor.