Firstly, big hugs!! It's extremely tough whether you're a first time mum or like myself, just had baby number 4.
Just my 2 cents... My first thought is that he's waking up straight away because he hasn't been kept awake long enough. I know in the early days babies fall asleep often whilst feeding but it's so important to wake them up so they get a full feed. Full tummy should help bub have a better sleep. So for me through the day I feed and if she falls asleep I will change her nappy and have a little chat with her. Once she's awake enough I continue the feed. I keep her awake at the most 1 hour and this includes feeding time. For example, if she wakes at 7 I make sure I'm getting her ready for bed by about 7.55 and down by 8. To prepare her for sleep, I wrap her and pop her over my shoulder and I pat her gently until she has sleepy eyes. Then I put her down and generally I give her a little bit more of a pat and then I leave the room. She's nearly 5 weeks old now and because I have stuck with it she knows the routine and often doesn't need me to go back in but in the beginning I would sometimes have to go back in and pat her a bit more if she got upset but now that doesn't happen very often. She has a bath about 5pm and then I feed her and start getting her off to bed about 6. She's normally asleep by 6.30.
Overnight I feed her, change nappy, finish feed, wrap and hold over my shoulder until she's burped properly then put her down in bed. It's definitely paying off as she's gone from waking two hourly overnight and sleeping on my chest, to now sleeping in her bed and the last two nights has only woken twice to feed.
Good luck, happy to answer any questions about what I've written as I don't think I've written it very well as I'm typing on my phone. Just remember, it will get better xx