I think to reach a good GCSE level over four months is possible, but requires a lot of work. Apart from immersion, learning by yourself usually takes longer, but if you work very hard, I'm sure you can reach a decent, but not great, level of GCSE-Italian. It's a shame you don't speak another romance language, or it'd be a lot easier! As long as you can get your head around italian grammar, I'm sure you won't have too great a problem! If you want any help, do PM me!
In bocca al lupo!