If you have been searching and applying for a job then just continue doing so and hopefully you will get a job.
It is very difficult to get a company to sponsor you to get a Tier 2 visa so most people fail in trying to get one (this is even when switching from a Tier 4 visa which is much easier than leaving the UK and trying to get entry clearance from outside). I remember back when I was in undergrad I knew several people who applying throughout their entire final year and the vast majority of them failed and it's not because they were not strong engineers or because their english skills were particularly poor, but because the employment environment for internationals is very tough. Obviously there were a few that managed to get one (thousands do it every year), but when you look at the official figures you can tell its tough. Only around 6K people or so switched from Tier 4 to Tier 2 in 2017 - even though the number of Tier 4 visas issued per annum runs at around 160K+. When the post-study visa was still in place pre-2012 the number staying on after their studies was over 60K per annum. I should also probably also point out that if you had an official sponsor funding your degree, that sponsor has to give you permission to stay on in the UK, a lot of grads still don't know this even though this rule has been around for a while now.
You might try the Tier 5 option but that option is very limiting as you can't switch from a Tier 5 to a Tier 2 from within the UK so it will prove tricky to get around that in a years time as employers will most likely be less likely to hire someone from a Tier 5 than a Tier 4 (this is especially true in the current environment where people need 45+ points to get a restricted Tier 2 visa granted). The wages that people on Tier 5's usually get are usually very low as they are usually just training positions (near minimum wage, unless you are a PostDoc), at least in the engineering space.