BIG HUGS!!! I am sorry you are having such a rough time! I was actually in the exact same situation you are in with my DD!
I think I read another post from you that said your DS generally sleeps well at night? Is that right? (I might be getting confused with another post I read) But if that is the case, my LO was the same way. She RARELY took naps over 45 min, yet she managed to go to bed without a fuss (most of the time) and STTN consistantly at 4 months old. I also felt like all I ever did was try to get her to sleep during the day and it was SOOO draining, so I really do feel for you. I finally did quit fighting her over day time sleep. I would try to fit in as many 45 min naps as I could. If she refused to go to sleep, I would take her out of the room for maybe 10 - 15 minutes (keeping activities low-key to try to avoid OS) and try again. Some times she would take a longer nap, but they were rare. I could never find a pattern with her and it really stressed me out. BUT I finally just had to make myself relax. I decided that as long as she was sleeping great at night, I wasn't going to stress over her few short daytime naps. She is 13 months old now and still isn't a great napper, but still sleeps great at night, so I can't complain.
If your DS isn't sleeping so well at night, then it is really important to try and get him to nap. I think at 3 months old, I always did a nap in the stroller. She would fall asleep anytime she was in there, so I took her for a walk everyday. It helped me relax and enjoy some quiet time while she napped. Even if the nap is 30 min, HEY, that's 30 minutes!
Also, I remember reading from a post when I was getting help for short naps that LOs sort out their nighttime sleep between 0-3 months and their daytime sleep between 3-6 months. Your son is still learning about sleep, so just give it some time and try not to stress. ( I know, easier said than done.
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Well, I hope something I said offered you a little hope. Don't give up! More HUGS!