@Murane I also have a 3 month old little boy, and it's my first so mostly muddling along as I imagine you are.
Firstly it's crappy your DH isn't more helpful but from your other posts it looks like he's working rather long hours despite this though you can't see him having him as 'babysitting' you are both parenting and have equal responsibility.
My little boy also needs a fair bit of entertaining, so I absolutely feel for you it can be absolutely mind numbing. I don't believe that as others have said were over stimulating or our babies would be entertained by a shadow as frankly he was amused by a shadow at six weeks and certainly isn't anymore
Are you doing any classes we've started one called discovery tots a couple of weeks ago I really like the class and it's given me ideas to amuse him as previously it was just making funny noises etc. We do baby yoga to nursery rhymes and he loves it.
Do you have a playmat/gym thing? I've recently found I can leave him lay on that while I put makeup on get dressed etc after 15-20 mins he starts to fuss as he's bored. We also play on it together every day and use it for tummy time. I've not found bouncers/swings any good I spent a load on a 2 in 1 and he hates it the bouncer alone is too low down he prefers being higher up to look around currently trying to sell it and get another that's higher up!
My little monster boy naps in the day if I'm out if he's in his pram/the car he sleeps the whole time really between feeds but at home he power naps for 15 minutes at a time which is a changed he's made in the last couple of weeks, I still put him swaddled and into his Moses basket for naps to maintain that routine and encourage a longer nap.
Sleep at night wise we've been spoilt he's slept from 1-6 every night since four weeks up until this week when he's worked out how to get out his swaddle but can't sleep without it. I've been up since 3 with him trying to get him back off, re-swaddling etc
I watch TV when he's having a feed, when hubby gets home could you go and have a bath take an iPad or a book and just take a relaxing hour to yourself?
Have you had any time to yourself yet, it's harder as your breastfeeding but a catch up with friends without baby even just a coffee for some adult time I'm seeing my friends next weekend for my birthday and literally cannot wait to be baby free and see if my brain still functions as I'm sure I'm losing brain cells daily.
It's healthy that you are honest about how boring and mind numbing it can be, I think those of us who can admit that will fare better on the long run and it doesn't mean we are bad parents. Sometimes I've text my husband saying the baby is being a (insert word you shouldn't call your newborn here) as I need that to get through my day!