Its bloody tiring, isn't it. Sympathy and coffee.
YOu can do either and see what works for you…
I am also a light sleeper and I find baby sleeping elsewhere for SOME of the night helps. On the other hand, if she is waking relentlessly (every 2 hours is tough) sometimes it is easier to have her right there so you don't have to get up. Sometimes (when she is next to me) I sleep with ear plugs in so I don't stir as much…
My general parenting philosophy is to have the ability to sleep in every room! Then you can mix and match a bit. We have a cot in her older sisters room where she starts the night, a travel cot in my room I can chuck her in, and the bed safely set up for co-sleeping with a side on it. So I can just see how the night goes!
I do think leaving babies who stir (not cry) is a good thing. Sometimes they do go back to sleep. I find as a general rule of thumb if the crying is quietening down they are settling. If it is escalating they are waking. A few seconds in the night can feel like ages, though!
If you have a helpful partner perhaps they would let you have undisturbed sleep for a chunk of the night and only get you if they were sure baby definitely wanted milk. Sometimes a cuddle is fine. Sometimes waiting until they settle back to sleep works.
I never found solids helped my babies sleep at all! In fact their sleep was disrupted after starting solids. So I would personally hold off for a bit longer. Babies vary though, of course.
I do think everything you've described is normal and riding it out is definitely a reasonable option. I also think you could try some gentle things if you think you're not coping with things as they are.
Daytime support is really helpful too. I get mates over for moral support (even if they have their own kids) - when my mum or boyfriend are around in the day I get a lie in, or a nap.
Take care. x