My advice would be to add more strings to your bow, maybe DBA, Programming, cloud technology specialist or Technical Project Management before moving on but when you do move on, go into the contracting market. I have worked mostly in the private sector but also the public sector as a consultant and as a contractor and to be honest, apart from more bureaucracy in the public sector, there is not a lot of difference. You still get the same issues around promotion and it depends on whether your face fits or you are in the right place at the right time, regardless of the effort you put in.
I was in a similar position to yourself years ago albeit in the private sector. Didn’t feel I was was getting the opportunities of promotion even though I felt I was good enough and out worked everyone in my department. I wasn’t the most academic but I worked so hard. I moved around the organisation over the 16 years I was there and in each dept I did well. I soon came to realise that due to the nature of the organisation (a merchant bank) and my cockney accent and lack of qualifications, unless I went to work as an FX dealer, which I didn’t have the aptitude or qualifications for, my only option was to leave, if I wanted more money and a better standard of living….glass ceilings.
I was asked to work for a consultancy as I had moved to the IT dept for the last 6 years at the merchant bank and had been the implementation analyst implementing a new finance system that the consultancy had sold them. My money increased by £10k immediately (this was back in 1995) and I was given a company car….the downside was I had a 2 1/2 hour commute each way every day for the first 3 months. They then sent me all over the UK, over to the States and Saudi Arabia. I stayed with them for 10 years and I learnt something very quickly….as a consultancy, they hired highly educated young people and once again the only way I could compete with them was to out work them. I also learnt that if I was to succeed in this cut throat business, I had to be bold and after 2 years there, I started to demand promotion, rather than wait for it. This had the desired effect and I quickly moved up the ladder. When I left in 2005 I was what they called an executive consultant, one promotion away from being a director. Money was very good for each promotion and the company cars got much better…….but they demanded their pound of flesh and I lived out of a suitcase.
When I left though, which follows on from @Jim Nealpost and where my point really is aimed at, I became a freelance contractor. It was the best decision of my working life and my only regret was I hadn’t done it sooner. Since 2005 I have never been out of contract, nor do I work every day that god sends. It’s not for everyone, it’s a massive step initially and you have to be totally confident in your ability and have to hit the ground running if you want to make a go of it. If you don’t, the contracts will very quickly dry up as contracting is an incestuous business.
My advice to you is if you go contracting now and please accept my apologies if I have this wrong, you will always be an IT Support contractor. That in itself is not be sniffed at and will provide you with a decent income but that is what you will be marketed as. It’s difficult as a contractor to change your job title as the hiring company want proven experience. If you were to contract as a DBA, Programmer, Cloud Specialist, Technical PM or whatever the day rate for any of those roles is very good.
Apologies for the long post but thought it would help you. Whatever you do, I hope it works out
All the best and good luck