My left tonsil is swollen and white spot next to it some healthtap drs say tht it wont go away without drainage-on penicillin past 24 hours its been swollen for 6 days Please can someone clarify this?

Well,... If there is an abscess, it may need drainage. If you simply have an exudative tonsillitis and that white spot you are seeing is the exudate, then it may go away with antibiotics (the penicillin) and salt water gargles, etc. There is no way for anyone to tell you for sure unless they do an exam on you and visible look at your tonsil.
Seeing Spots. The tonsils are like two towers manned by soldiers to keep watch for invaders. The folds in the tissue (crypts) are like staircases on the outside of the towers. Occasionally food particles, saliva, and bacteria collect on these stairs and form "white spots" which are debris that has hardened. These are foul smelling and can irritate the tonsils. Manual removal usually helps to resolve issues.
It depends. If it is Tonsilitis it will take more than 24 hours to improve. If it is Peri-tonsillar abscess ( Abscess around the tonsil) it needs drainage ASAP.