Hi and welcome!
Yes, you can get bartonella from a cat. Bartonella hensalae is also referred to as cat scratch fever. The red marks are typical of bartonella. Bartonella also causes bone pain, headaches, recurring low grade fever, sore feet, all manner of skin symptoms including itching, and much more.
I did not get sick enough to know I was sick until 2009 at age 39. I did not know about Lyme until this year when I tested positive for Lyme and ehrlichia. Once I started learning about Lyme and all the coinfections, I recognized that I'd had many of the bartonella symptoms since early childhood. I have deep creases across my abdomen that get reddish purple and feel irritated at times. Other times, they just look like deep creases. I know I've had them since school years because I remember feeling the skin irritation when slumping over my desk in school. My mother used to fuss at me telling me I was making deep wrinkles in my stomach from slouching all the time. (Yeah right.)
I also developed stretch marks on my thighs around age 10 or 11. I had no sudden weight changes or growth spurts, so completely unexplained. They are still there but have faded over the years. Now they're mostly visible only on my buttocks and hips. When I was young, they were clearly visible from my knees up to my butt. The ones on the outer thigh where white and raised like scars. The ones on the inside of my thighs were reddish purple and looked like a pattern of engraved lines about 1 inch long all up and down my legs.
I had leg aches since early childhood, mostly at night. The doctor told my mother they were growing pains. I never outgrew them. They did not stop until I started going to a chiropractor a few years ago. I recently had it again one night last week. It shocked me. First time I'd had it in a long time. It also reminded me of how much pain I endured throughout my life. As horrible as my symptoms have been and as much pain as I've experienced in the past year, the pain from those leg aches is far worse to me than any of the other kinds of pain I have (headaches aside). I can't deal with that aching pain without pain reliever. I took Tylenol on a nightly basis for decades. I learned that I could often fend off the nighttime leg pains with Tylenol. If I waited until it happened, it would keep me awake for hours. (I don't recommend pain reliever now, though. It can damage your liver.)
Had headaches since age 9. Have had recurring low grade fever off and on for years. Have a lower than normal temperature. Have had night sweats off and on for years (not sure if this is bartonella or babesia, though). Headaches can be either one, too. Some experts say bart headaches are more painful and babs headaches feel more like pressure than pain.
Lately since trying to treat Bartonella with Stephen Buhner's herbal protocol, I've had bouts of itchy bumps on the backs of my legs. I'm sure others can tell lots more. I'll stop with this.