I've been through the redundancy roller coaster after working for the same company for 24 years. It was my first job at 19 years old and in my mid forties had no idea what job hunting would involve.
You have lots to do/prepare. 3 months notice is no time at all. Each time you find a job to apply for, apply for it, wait for closing date, get an interview, potentially a 2nd interview then wait for an answer/offer back several weeks will pass.
Get your CV up to date, update linked-in (don't expect to be headhunted, jobs you apply for will check your social media presence), check and tighten your facebook settings so only friends can view, research competency based interview questions and start writing up and practicing answers (look up STAR technique).
Start finding out where you can look for jobs, research local-ish companies in your area that you would want to be employed by (there are registers somewhere, might have been a national library site I used, where you can search for companies in your area - many you wont even have heard of) and find out if they have a careers website you can register with so you can apply for jobs directly rather than through a recruitment agency which costs them. Think about how you would write speculative and specific applications.
Start applying for and going to interviews now. Even if you cant take up the role the interview experience will be invaluable. When I was made redundant it took a good 6 interviews before I stopped being a complete nervous wreck at interviews as I started to understand the process more. I missed out on a few jobs I would have been perfect for by totally fluffing the interview.
I had a 3 month notice period too, but was told about the redundancy 6 months prior to leaving as they needed me to manage my exit, train up those staying to be able to do parts of my role (it was a mass redundancy and they tore out layers of experience/massive cost cutting). It was sole destroying especially towards the end, but I had to stay for the money and additional 3 month retention bonus, when I had no actual role to do but had to stay to be available for any questions/issues and I spent that time preparing.
In the end I was lucky, from my research I found the most attractive companies to work for in my area were either FMCG or life sciences which I had no experience in. 6 weeks after leaving my job I took a 6 mth fixed term contract to back fill someone in a much much lower paid role. At interview when they asked why I was applying I told them, how I had a passion 🤦♀️ to work in FMCG and why, I was taking the role for experience in this area so a fixed contract in a front line role was ideal. The role was extended to 1 year, then a permanent job more in my previous area opportunity came up which I was asked to apply for and got. Been there for 7 years now.
Also remember to sign on with the job center, even if you don't need the job seekers allowance. It is a pain in the arse going in, they are as much use as a chocolate teapot and bring you down, but there was something during my recruitment at my current company that was made easier due to the fact I had proof of my employment history and registering at the job center was included. I can't remember exactly, it was something to do with some compliance for their listing in US/terrorism prevention etc, it was required even though I had no intention of US travel with work.
Good luck, it will be a tough few months ahead.