I totally understand your situation, mandymac. No, you are not overreacting and it's not jealousy. You are trying to set initial boundaries for what could get out of control later. I know because I am in the same boat, except I've been with my boyfriend for almost 2 years. I wish I had better news.
My BF has a daughter with his ex and she texts him constantly, even though she has a steady man in her life and a high-paying job. She will text about her feelings - good and bad, her house, her dating problems, ask him how he's doing, send pics when she's out with friends at night, on and on. She will call late at night because she can't get her daughter to sleep and will blame it on him or expect him to do something about it over the phone. If this is going on in your relationship at 3 months, it will most likely continue if he allows it. I thought his ex would stop once she found someone new, but I was wrong. My BF does not set boundaries with her and responds to all of her texts, no matter how inane. I thought he would change. I've told him many times how unhappy this makes me and he should ignore her unless her communication directly concerns their kid. We've had arguments about it. He claims that he doesn't want to upset his ex by not responding because his daughter lives with her and needs a happy mom, and he says it doesn't bother him. All of this kills me. I recently checked is text messages from her on the sly and found that she asked how he was doing again. He did try to deflect and remain distant, but she kept going and told him she can't help that she cares deeply for him and and she will always be there for him if he needs someone (she divorced him 3 years ago, but left him and their daughter alone for two whole summers while she pursued her career options during their marriage - so no, she does not care deeply for him). He responded, "Thanks, same." I believe she has a mental disorder or personality disorder. I ignored the signs at the beginning and I kind of regret it. I didn't want to seem controlling or jealous right off the bat, so I tolerated her outbursts over every thing we did together and his trips with her to "spend time" with his daughter (not day trips, they went out of the country together for a week, he spent 5 days with with her over Christmas, etc). He kept assuring me it would get better and she would relax once she realized I wasn't a threat. Nope. He even blamed me for not being more "cooperative" and letting her get to me. I've considered leaving. If a man doesn't want to acknowledge that what he is doing is enabling his ex's behavior and disrespecting you in the process, then you don't have control of anything and it will only get worse.