Taking people places then showing them the escape routes is not a good way to get over panic attacks and anxiety disorders. You can easily build up more and more reassurances like that until you spend your life addicted to these little crutches you've set up for yourself. Some things aren't escapable and people with anxiety need to deal with those things as well.
You do not get over panic by knowing the escape routes, you get over it by not wanting to escape and not always desperately searching for a way out of a situation.
Essentially it comes down to changing your pattern of behaviour by teaching yourself that when you panic, nothing bad will ultimately happen to you. I'm afraid the only way to do this is to expose yourself to situations that terrify you and gradually learning to deal with it by making it less and less easy for you to escape, for example:
Going somewhere with someone who doesn't know about your anxiety so you can't ask them to distract you or calm you down.
Going to a place where it's difficult to get back from quickly- maybe somewhere further away than you'd normally go.
You need to recognise what escalates your panic and what reduces it. People have already mentioned breathing exercises which are very helpful. You should practise these even when you're not nervous to learn what it feels like to be calm and how to calm yourself through breathing so that you can apply to situations in which you panic.
Recognising what your body does when you panic is also essential. When people get anxious they start analysing their bodily functions which escalates the problem. Being able to stop thoughts such as 'I'm going to faint', 'I'm going to embarass myself', 'I'm going to die' is very important in stopping yourself panicking. The better you get at noticing these destructive thought processes, stopping them, and consequently calming yourself down, the easier you'll be able to reduce anxiety when you're out places. Once your confidence to do this increases then you become less and less worried about going out in the first place because you know you will be able to deal with it.
This could just be a bit of a phase (a lot of teenagers suffer from spells of anixety) however anxiety disorders are very hard to get over and often never completely go away. This is why it's so important to learn to cope with it before it starts to adversely affect your life.
Either that or take truck loads of valium, they're both fine choices.
PS I can't be bothered to proof read that, so apologies.