California tan has a product called " INSURANCE" and it is basically for over exposed skin to the sun , to help ease the pain of a sunburn because it sounds like you did get a slight sunburn. It is Aloe based with, cucumber and calendula to help calm, cool and relieve the sunburn. It is a great product and is also a good
moisturizer .
Start to build your tan slowly especially if you are fair skined and yes you should use a lotion. It will help you develop your tan and also keep your skin moisturized and you should also moisturize after you shower. Dry skin can DEFLECT up to 40% of the UV rays in a tanning bed.
Ask the person who works at the tanning salon you go to to maybe put you in a starter bed, or use the bed you used but do your tanning sessions in less time, maybe 4 or 5 minutes every other day or every 2 days and then as your tan starts to develop you can gradually increase the time in the bed and the frequency you go tanning. In time you might be able to go for the entire 10 or 12 minutes the bed allows you to go.
Good luck and remember...start out slow and MOISTURIZE !!!
Have a good day !
Ricky