Hi OP, FWIW I'm an academic specialising in Russian foreign/security policy. These are scary issues and so it's not surprising that you and other people are anxious. Hopefully I can explain why you don't need to worry about this particular issue very much. Tl;dr: the Russian army isn't suicidal so I don't see them using them, even if Putin wanted them to.
There are two types of nuclear weapons that people have talked about Russia potentially using during the war. The first are the missiles designed to strike western Europe, including the UK. These are the things that the fascist nutters on Russian current affairs TV have been threatening to launch at the UK and Ireland. This is delusional nonsense that no-one believes, including them no doubt. Any attempt to target a NATO state with a nuclear weapon carries the very high probability of a nuclear response, wiping out Putin, the senior Russian military leadership, their wives, mistresses, children, dachas. Putin knows this. We can never say anything with 100% certainty, but this is as close to an impossible scenario as it's possible to get in international affairs.
The second are the so-called tactical nuclear weapons, designed to be used on the battlefield. They're referred to as this because the idea is that they only have tactical application and effects - basically, they're used to achieve specific things on the battlefield. They are, in theory, different from strategic nukes (the type I mentioned above) which transform not just the battlefield, but the states involved - and the rest of the world.
The problem with the idea of tactical nukes for Russia in this scenario is that they can't, in fact, contain their effects to the battlefield alone - i.e. tactical nukes can never actually be tactical, they will provoke escalation and so will always have larger, strategic effects. This is a point made by people like Lawrence Freedman, one of the UK's most eminent scholars of war.
We can see this very clearly in the current war. In relation to the nuclear power plant currently being occupied by Russia, Western politicians have said that a deliberate release of radiation by Russia could be treated as a NATO Article 5 matter - meaning that it would provoke a direct military response from NATO (most importantly, the US). If that's the position in case of the power plant, you can be very confident that the same principle applies to any Russian use of tactical nukes. More importantly, the Russian government will know that it applies to tactical nukes.
We don't know what mental state Putin is in - it's possible he might feel the game is up and be happy to go out in a nuclear holocaust. But the men (and they are all men) around him are in power for what they can get - status, and a yacht-load of cash. Shoigu, the Russian Defence Minister is the classic example of this, but they're all the same. I can't see any circumstances in which the men around Putin would be willing to kill themselves and everyone close to them just to allow Putin to avoid defeat. They will get rid of him sooner than do that.
Another factor making tactical nuke use in Ukraine massively unlikely is the morale problem in the Russian army. There are all sorts of reports (not all verified) coming out about the state of the Russian army in Ukraine: desertions, soldiers disobeying orders, resignations, serious tensions between officers and men, fighting between the Russian army proper and the units from the Donetsk and Luhansk "peoples republics", fighting between the Russian army and the Chechen irregulars. It's clearly an absolute shitshow - as can be seen from the way the Russians collapsed in the face of the recent Ukrainian offensive. I don't see how the Russian army leadership (even if it wanted to) would persuade underpaid, underfed, mutinous troops to use tactical nukes, knowing what the response would be.
Hope this all makes sense. Happy to explain anything else Russia/NATO/war-related you have any questions about.