In the future you should always contact the police, even if it's just to have them verify that the other party did not have any damage. But it is extremely helpful that you took photos.
Even though you don't have much damage and the other party had little to no damage you should still contact your insurance company so that they can resolve the issue and you don't have to worry about any future problems or have it hanging over your head that something could happen.
Your premiums are likely not to be raised if your insurance company does not issue any payments out on the claim or if they do and it's a minimum amount it should not be increased. It will depend on your state, prior driving record, amount that is paid out, how long you've been with the company, your age, ect.
Because you didn't contact the police and you weren't issued any tickets (assuming the police weren't there) you should not have an impact on your driving record.
DO NOT settle the claim with the other party in cash...it is a very bad idea. Because if you settle it for cash they can still try to claim under your insurance party at another date. If you do settle the claim with them for cash make sure you have clear documentation, something notarized, that you did pay them so they can't come after you any more then what you paid in cash.
If you do need to get your vehicle fixed find out how much it will cost and what your collision deductible is. If the cost is going to be lower then your deductible then just go ahead and fix the vehicle yourself, there'd be no need to have you insurance company involved in fixing your vehicle if the damage is below your deductible.
Professional Claims Adjuster