Sister telling entire network of family and friends im a liar and a fraud...

Guys.. weird deal.. My sister had created a company and hired me on briefly to provide design services. She started being really demanding like asking me to get 30 graphics in in a week... Demanding so much that sometimes I couldn't keep up.. it took me working sometimes till midnight 2 weeks in a row type thing.. but the graphics were good and her clients were happy.. But a few months into it.. It got to be a lot and she truly couldn't pay me on time.. or sometimes at all... so i did what id been wanting to do for a long long time.. I've worked for several fortune 500 companies in marketing in bus dev.. and I understand and have experience with marketing.. sooo I combined all of that together with this weird feeling that my sister was going to fire me.. and created my own company. Very different from hers but some services we did offer like social media management... and all of sudden it was this.. I betrayed her.. I lied.. am a horrible person.. all of this stuff.. it was awful...well its bled over into a client that we are both providing services too.. The client has asked us to buy books of hers to boost her numbers.. and because i was the one who put the numbers together telling her what that would take to hopefully make a list.. she made a comment about just asking a pathological liar.. and then laughed with my sister...That I guess.. Im the liar..even though she asked for the project and is funding it...My sister has also said all of this stuff to my mom.. That i'm a liar and also a fraud... just horrible stuff.. and whatever shes saying is working because now my mom has asked me straight up if i'm lying to people.." like what?????!...my business is going so well.. im learning a LOT about marketing.. and admit it didn't know it all and still don't.. But know enough to help people accomplish their goals.. I have 4 very happy clients including a health clinic with 10 locations, a huge apparel company, an exec from a top 5 tech company, and a dermatologist office... and I just hired my first employee etc.. i just cant wrap my brain around that Because my sister felt SO betrayed and I guess couldn't handle the me starting my own business.. The best way she knew to bring me down was to call me a liar and a fraud to not only me.. but all of these people im close with.. And ill admit I can be an introvert. so maybe i don't come off as the most bubbly person.. But i definitely am none of those things.. Im blessed with a good head on my shoulders and a wonderful relationship with the lord.. I feel he has blessed me and is pushing me to keep going with my business... I dont know how to manage these accusations.. .. im floored and truthfully just sad.. Very very sad that my sister would say these things and make me out to be this horrible person because she couldnt handle that I took on a line of business that her company also provides.. not to mention im on the complete opposite side of the country completely avoiding her "sell zone"...and ive never stolen a client or anything... Just awful. And weird. and sad... any advice? how the hell do i keep my head up...