I've been on penicillin for 3days now 4x a day for tooth abscess I'm starting to feel better does this mean the infection is under control?

NO. This means the infection is lessening but not gone. You must follow-through and get the treatment required to address the cause. Otherwise it will again worsen and you always run the risk of losing the tooth. Be wise and get the treatment needed. Good Luck.
Infection. No! the infection is merely in check. The only way for it to be irradicated is by root canal therapy or extraction of the tooth.
Controlled yes. Your dental abcess is controlled for now. It is not cured. You still need to treat the tooth, the source of the infection or it will return. Follow up with your dentist and get the tooth treated.
See a dentist ASAP. If you rely on antibiotics or other not a definitive treatment, the tooth infection always will come back. Dentist/oral surgeon will treat a tooth infection by treating the cause and getting rid of the infection. Do not delay. See your oral surgeon ASAP. Good luck.
Probably for now... It usually takes 12 to 72 hours for an antibiotic to knock an infection down enough to provide relief. If the underlying cause of the infection is not addressed, pain and infection can return after antibiotic treatment is completed. Therefore, it is important to see a dentist to determine if the underlying cause of the infection can be eliminated.