generally, you can apply for asylum in Italy. It is a EU-country and the asylum procedure is regulated by the EU-guidelines, so I beleive, the authorities in Italy are obliged to take and procede your application. How this procedure is arranged in detail, you better ask in a special councelling center for asylum seekers and migrants in Italy (the best - in the area where you live). Perhaps they can recommend you some other possibilities to stay through finding word or further qualifying. For asylum you generally must have very serious reasons. The praxis of acception or rejection of the asylum applications from different countries differs sometimes very strongly in different EU-countries, therefore you must ask local consultants if you can have a good chance. Do it before you make your asylum application.