Getting baby to sleep longer

Rebecca

My 13 week old was going longer between night feeds until he got bronchiolitis at the beginning of January and spent 3 days in hospital where he was getting fed little and often since then he has been waking every 3 hours in the night. He goes to bed between 6.30 and 7.30 then will wake for a bottle between 10 and 12 then again at 3 and then he struggles to settle well after that. He's also cutting his 2 bottom teeth so I think that has something to do with it but does anyone have any tips on how to settle him that doesn't involve me having to cuddle him for ages like I do now and how to make him go that bit longer between feeds. Thank you in advance from a very tired mama!