There are three things that could be causing you a lot of pain on your gums. I' help you figure out which one it is and what you can do about it to get relief.
(1) Canker sore (aka aphthous ulcer or traumatic ulcer)
If the sore is red around the border and white in the middle, then you probably have a canker sore. Some people get them spontaneously (aphthous ulcer) and sometimes they're cause by accidentally irritating your gums (traumatic ulcer). Small ones can heal in a week or so and larger ones can take up to six weeks to heal! Canker sores tend to occur on the inside of lips, tongues, and cheeks, but they can occur on gums as well.
Treatment for canker sores is palliative, meaning we just try to keep you comfortable while your body heals. I recommend Kank-A, which delivers some local anesthesia and can form a kind of temporary band-aid over the sore. Your dentist can also offer some helpful treatments. Avoid tobacco products and alcohol (including alcohol in mouthwash) to speed up the healing process.
(2) Infection (aka abscess)
If the sore is red with a small white dot or bump in the center, then you may have a tooth infection. The infection could be from the nerve of the tooth (endodontic abscess) or from the gums themselves (periodontal abscess). The white dot/bump in the middle is the draining infection, kind of like a pimple. You may also notice a bad taste or odor in your mouth. You may also have other symptoms, such as pain to biting or sensitivity to heat.
If you suspect that you have an infection, see your dentist to confirm the diagnosis. They will probably want to run some quick tests, including taking an x-ray. They may also prescribe antibiotics, depending on the treatment plan.
(3) Other pathologies
There are other things that can cause painful sores on your gums, including viral infections or just really inflamed gums. If you're in a lot of discomfort or are worried, see a dentist right away. If you choose to wait it out to see if it resolves on it's own, please do not wait longer than two weeks. And if the sore comes back again then see your dentist while it's still present. Don't freak out, but dentists also need to make sure that these sores aren't cancer or a pre-cancerous lesion.