Greetings Kaycee12! A 5 star review infection control specialist could be consulted if desired but everyone is in charge of their own health care. The infection has probably gone deeper than the surface according to what symptoms seem like and could end up being a problem to walking if not taken care of. Squeezing in my opinion can squeeze it deeper and I would not do that. Tea tree oil tablets might be useful if desired but I would not use them longer than about 2-4 weeks as some contain copper, which is a metal and the other one has zinc. Zinc can be good at first but an overabundace can lower the immune system over time.
A steam acitvated charcoal pack might draw out the poisons of the germs and the pus as well. This can be made by taking the steam activated charcoal powder (not the briquette for grilling) and placing 2 tablespoons of it in water and 2 tablespoons of flax and mix it, simmer it making a medium thick paste and place it on a paper towel to within on inch of the border. Then I would place it on the wound after it has cooled so it will not burn skin.
After the pus has decreased and come out with the charcoal pack I might try using a warm shower on it for some time about 3 minutes and alternating it with cool 30 seconds or even warm wet towel on it then an ice cube 30 seconds.
I would do healthy lifestyle things. A daily walk in sun and fresh air before ten o'clock in the morning and after two o'clock in the afternoon might be good. A daily extra rest before meals but not after as this would encourage fermentation of the food. I would avoid refined sugar like the plague it is very bad for the immune system and will not help a person get well. I might use more grapefruit, lemons, limes, garlic and onions (vegetables should be in a separate meal from the fruits though.