Can toothpaste actually work on acne?

No it can not. Toothpaste as name states is for teeth, get the proper acne meds to treat acne-;).
No. No. Toothpaste only belongs in the mouth because it can burn your skin. Use an astringent that has salicylic acid in it.
Get a real Rx. This is the 21st century. If topical benzoyl peroxide 5% 2x/day hasn't cleared you in two weeks, get prescription-strength treatment from your physician. The medications for all but the most severe cases are inexpensive and safe.