Desensitisation, when a dog is young, helps because if you do it right, you are desensitising to all sorts of loud noises (even if firework noises are one of the ones you pick) and thereby making it less likely that the dog will find a brand new type of loud noise scary when they are older. They generalise the learning. Mostly. But this is not guaranteed.
There is some chance to do the same work when they are older but I think it unfair to set an expectation this will definitely work with any dog. That just isn't the case and there will be dogs that have developed a speicifc fear for the specific noise fireworks make and no amount of recordings is going to replicate it. Not least, because there is often a detectable vibration that goes along with the truly loud firework noises. Unless you are about to upset your neighbours with an advance sound system turned up loud, you will never make the windows rattle with a recording.
I personally hate the way dog training is sometimes talked about in absolutes. For eg whilst it is true that puppies born on the run up to firework night tend to display less fear to the noise when they are older, this is not a guarantee and some puppies born during this time do go on to develop fears. They are complex little beings and you just cannot have absolute rules about complex creatures.
Similarly, it's not true that you must never reassure a frightened dog. Yes, dogs do sometimes take their cues on behaviours fom us and so for some dogs, sometimes, a relaxed attitude towards fireworks can help them learn the same - this is mostly true when the dog does not yet have an ingrained reaction. But you cannot reinforce fear and I would hate to think someone would not comfort a scared dog out of worry they are making it worse fot the dog. That's not fair to the dog for whom reassurance can be helpful.
OP, there are very few OTC medications that can really help to be honest and most have a doubted success rate, regardless of manufacturer claims. Zylkene MAY help, but it really is better if it's had time to build up in their system and even then the jury is still doubtful. Your best bet for this year (if you really cannot afford a vet) is to create a safe space for your dog to hide (comfortable, warm, dark and enclosed) and have constant soothing music on at a level that helps drown out a tiny bit of the noise. Follow your dog's cues as to whether or not having you there comforting them seems to help.
Plan for next year - which for best results does mean a vet consultation and effective prescription.