When you have sex the first time, or even first few times, it is normal to spot a bit. It is normal as long as you are not bleeding a lot, like a period or more. The burning when you pee is more than likely a UTI (urinary tract infection) or bladder infection. This can be caused by bacteria entering the urethra while sex. These infections are common, and can be cured. You don't necessarily have to tell your mom that you had sex. You can get these infections from other things besides sex. Wiping from back to front can cause them, drinking a lot of carbonated soda can cause them, and many other things. If it continues, you may need some antibiotics. For now, you can try drinking cranberry juice...this is an old home rememdy and can help with some of the symptoms.
You have a UTI, as what amberette said can you get a UTI from other things...not just sex. The antibiotic is really easy to its usually a pill for 5-10 days. Until you go to the doctor drink just water and cranberry juice-make sure it is 100% juice too. If you don't like the juice you can buy it in a pill form made by AZO. Stay away from soda and sugary stuff, and sometimes citrus can irritate the urethra. Just tell your mom that you think you want to go to the doctor for peeing...I'm sure she'll understand. All you'll have to do at your doc office is pee in a cup! So no worries, don't suffer when you don't have too!