Long, long ago, with my then baby son, I left an addict who got physical with me (just once), though there had been considerable verbal abuse previously. I had nowhere to go & the police directed me to a domestic violence shelter/safe house. Like you, I felt like I didn't "qualify" for the services, because it had only happened once.
I ended up living there for 2 months. During that time I went back to college, did therapy & groups in the house, found childcare for my son, & found an apartment with another single mother to move to.
Isn't that the point of domestic violence services? To help you build your new life successfully, so you don't have to go back.
I'm sure all the counselors & workers who helped me felt satisfied & proud that I was successful with their help!
I went on to do much additional support work with survivors through my lifetime, & gave that love & care back to the world many-fold.
Interestingly, of all the women (with children) who passed through that house in the 2 months I lived there - every single one (besides myself) returned to her abuser. The horrific abuse in their relationships was so entrenched that they couldn't imagine another life at that point. I learned a lot from that experience, but one of the things I most valuably learned is that leaving right away when it starts means you don't find it familiar or comfortable, & that is a very good thing.
Receive & give, give & receive. It is just right for you to receive that particular care from people who specialize in it, for now...