I could have written your post myself in early December when DS was 14 weeks old. We had a few weeks of refusing to feed to sleep except when he would, which was exhausting for all concerned as he didn't have a plan B and would get very frustrated. At 5 months, he will now feed to sleep again, though success is variable if we're out or there are distractions. So it might be a phase.
My friend had the same problem but her baby still refuses to feed to sleep so she has had to work on alternative ways to settle him. Unlike my DS, hers will self-settle at night not that I'm jealous or anything.
Like you, I find he's often tired after a short nap but refuses to go back to sleep; I try to ride with it and just bring the next nap forwards but that doesn't always work...
Solidarity
here, it's hard work. We have tried formula and expressed milk in case the problem was hunger (it wasn't), dummy, rocking, shush/pat in crib, pick up/put down, swaddling (not strictly recommended at this age if you've not done it before so do your research), and even car seat (probably not recommended but thought rocking in it was worth a try surprised the neighbours didn't complain
). The only one we've had any consistent success with is rocking, and only when very sleepy - I usually use it to re-settle, not ideal but anything else leads to Total Outrage and only boob will do then.
When we were at the height of the not-feeding-to-sleep phase, we had marginally more success getting DP or my mum to resettle by rocking/picking up/cuddling than me. Probably due to the milk smell. Something you could try, perhaps? Mine also thrashes around and sometimes needs to be almost held still, it's as though he's physically fighting sleep.