Your question is a hard one to address. Does it hurt to get a cleaning it may a little if you never had one done before. What may be a bigger issue is that by not going to the dentist you may need more then just a general cleaning.
Should you go to a dentist?…. Yes. However, maybe there other factors that your mom must deal with that makes it so that she can not for whatever reason send you to a dentist. If so, it may be easier for her to say what she did.
With that being said you can either wait until you are 18 and pay for the dentist yourself, and in the mean time take extra care of your brushing and dental hygiene. Or you may want to speak to your mom one more time. Explain to her that you would really like to be able to go to the dentist. However try to understand if she still will not take you. You are not in her shoes to know her full reasons.
Good luck to you