I had this trouble a while ago, I just hate my upper arms so I didn't want a strapless dress and in the end I found a really pretty one from Monsoon with quite short sleeves but still covered the bit I didn't like! I don't think you
have to wear strapless at all as long as its appropriate for the occasion.
As for the make up thing, you can walk into boots or debenhams and get it done, I'd be very suprised if they do one eye one colour and one another! Just say that you're interested in their products and they'll do it all for you. Or say that you have the products but you're going out and you'd like them to show you how to make it look good. A teeny weeny white lie never hurt anyone! lol
Have a nice time

xx