Every individual concern you've brought up in this thread is valid and not uncommon. The important part that @ramble81 is focusing on is that your mindset on how you approach these challenges is incredibly unprofessional.
Having more to do than you realistically have time to do is the reality of working in IT. Everything the business does ultimately comes back to IT at some point in the process, so we naturally have to work with every single branch of the business.
Being underpaid is a reality of work for most people in the modern world. The professional thing to do is to decouple your feelings of how you're being paid from individual tasks or duties that are expected of you. "I'm not paid enough to deal with this" should be limited to tasks outside of your scope of work. If you're ultimately not paid enough to do your job, complaining about individual tasks that are part of your job being bnove your paygrade is just saying you aren't willing to do your job. I can't tell you the best solution to your pay situation. Maybe changing jobs or even changing industries will help, but also changing your mindset can do wonders for your mental health. For example shifting to instead saying to yourself "I'm woefully underpaid but at least I'm working in IT and not at X" can greatly help ease the pain until you reach whatever milestone which does help improve your situation
What you need to do regarding your workload is have a conversation with your manager/superior about prioritization. You say "hey, I have this this this and this that need to get done right now and I can't realistically do them all, what do you want me to prioritize and deprioritize" and if something important hasn't been given priority in a long time (such as patches) you need to then push back and say "we haven't been able to apply security patches in quite a while, I think we should reprioritize this so we can put some time into patching this week" this is how you manage a gigantic workload is by shifting priorities. The longer important maintenance tasks are ignored, the larger the impact and the harder it will be to complete the tasks