5 weeks isn’t enough to see much of anything, let alone the full results. This is especially when you’re not using minoxidil at therapeutic levels...
minoxidil needs to be applied twice a day to hit that threshold. Anything less than that is pointless, except in the case of anecdotal unicorns. I would be concerned, given your scalp inflammation, that you may not be able to tolerate it, but there’s only one way to find out...
Not time to shave yet, but you need to use what time you have to figure out how much your hair is worth to you. minoxidil offers, at best, cosmetic relief from the blading process but doesn’t do anything to slow it down or stop it. The only way to do that is finasteride/dutasteride both of which come with a lifetime commitment and a long list of possible and probable side effects. Only you can decide whether or not the risks are worth it for a chance at holding on to what hair you have left.