No, it won't recover. I had the exact same injury. I also naively thought that they would take off the plaster cast and that's it, I'll be like new. But no, another week almost on crutches and a couple of weeks with a cane. At the same time, I was helped to develop a leg by the professionals from the sports dispensary, who know a lot about rehabilitation. Baths, massage, physiotherapy, currents, etc. Still, it took almost three weeks to recover partially. Reschedule your trip if possible. Lame and tormented, with pain and a swollen leg in the evening, a bad sleep, you won't get a high from Italy.
I don't want to upset you, but it's guaranteed not. I highly recommend consulting a doctor, and apparently make a decision to postpone the trip. In any case, you will need a month's rehabilitation, during which there can be no question of traveling.