Is there a home treatment/remedy for an infected tooth?

Only temporary. Clove oil/anbesol or similar otc preps can ease pain temporarily; nsaids like aspirin/motrin/aleve/etc (if your stomach tolerates them & you're not on a blood thinner) can further reduce pain & inflammation, but for definitive relief, you should see a dentist for treatment; antibiotics may be sufficient, but if there is significant decay, the tooth will need additional work (filling/root canal/.
Not really. Drug stores carry some numbing gels that help some with the pain, but not the infection. You should really see a dentist to get it treated.