With all my clients I get them to fill in and sign a form detailing any allergies, colds, or other illness they may have and details of their doctor/GP. This is to cover several things:
1) If my client says they have an allergy to an ingredient in makeup/skincare it means I can either try to use any makeup that doesn't have that ingredient in or I am entitled to refuse them service. I don't want to give them the blotchies or worse!
2) If they don't admit to any allergies and then they say for example, tried to sue me after suffering a reaction I'd have all the proof I needed to say that this person signed to say they had no allergies etc. whatsoever.
3) If they have a cold it means I can refuse service. Not only does doing their makeup when they're ill put me at risk but it puts my other clients at risk if I go and do their makeup thereafter. It also could mean I'd be unable to do my work for several days losing business and cancelling appointments etc.
4) If they have something more serious like conjunctivitis/wart then it means I can also refuse. I can't risk spreading these. Despite using alcohol to clean my entire kit before each new client, you don't want to take your chances!
I have a friend who nearly did makeup on a lady who said she was merely suffering a slight tickly cough after a flight back from Kenya. My friend, although she had turned up ready to start, said she couldn't carry through and would have to go home and come back when she was feeling better. The lady was very insistent that she was fine but after she visited her doctor it turned out she had some sorta bug from Kenya and she had to take antibiotics - so go with your gut instinct, if you're not sure don't agree!
Of course you don't have to be awkward about it - I simply explain to my clients I just need them to fill it in (standard procedure blah blah blah) and it normally comes across like I'm also making sure I put them at no risk and they're in safe hands etc.
I've not yet had an unhappy customer (touch wood), but of course you can't please everyone. One of my first wedding trial appointments the client had some constructive criticism and luckily she was very nice about it (some people might not always be) but I took it in my stride and went with the flow making sure to let them know I wanted them to feel their best. On the wedding day itself they were very happy and even sent me a very kind thank you letter!
I usually pop nice little extras in like give them a free brand new unopened lip gloss in the colour that has been chosen for their wedding day so they can apply throughout the day and keep for future use! It's often the nice little touches (freebies etc.) that go a long way. I think if I ever got a complaint I'd be very apologetic that they felt that way, offer a way to go round the problem and then offer a free piece of makeup to say sorry and thanks for your time...
HTH! x