My DD is 4 months and is almost exactly the same. I try & fob her off with a dummy/giraffe to chew, pat her chest & shush her. Sometimes it works, sometimes it doesn't!
I don't want to scare you, but we were doing all that at 3 months (except the middle of the night feed was more like 1:30am), and I could just about cope sleep-wise. But then we went through the dreaded "4 month sleep regression" where after her 1:30 feed she would wake EVERY HOUR for no good reason: she had a full tummy, a clean bum, no wind, she just wanted to play. When i went into her she would literally laugh in my face which, despite the hideousness of the time, was soooo cute. I'd pat her & shush her & she would usually go back down.
We had the hourly wakings for about 2-3 weeks & are now back to getting up at 2ish & then at 5:30-6 which by comparison felt amazing!
Hang in there OP. It does get better. Previous posters have suggested some practical things such as dropping dream feed or moving bedtime which hopefully may work for you (although didn't for me). I always leave DD for 5 mins to see if she settles herself & if not I go in and pat, shush, out something in her mouth etc
Is DS in his own room? That was the first thing the health visitor asked me when I cried on her during the sleep regression. It's annoying having to get up and go into them, but it does make it easier to ignore them!
Good luck.
It will get better.