How do I calm myself down?

Ok I'm 20 years old and I suffer from pretty bad anxiety, I take no medication for it because I previously took beta blockers and anti depressants and I hated them. The problem is that I'm going to stay with my dad in london tonight and tomorrow night. The first issue is that I'm freaking out about the drive because it's the longest journey I've done on my own and I'm terrified that I'm going to have an accident because it's mostly motorway driving. The second issue is that people keep going on about a terrorist attack tomorrow and I'm literally going to be taking the tube and hanging around central London all day. I can't change any plans now because my dad is a major control freak and he will go crazy if I change our plans, he gets angry VERY easily. I just need some tips on how to chill out and stop freaking out about everything because the last time I got like this I had a major meltdown. I just end up convincing myself that I'm going to die. Thanks.