Many people hold you are allowed to shave every friday during sefira, provided that there is a ???? that you are still doing aveilus, which seems to mean that you are shaving less frequently than you usually do during the year. (I don’t have time to find the mareh mekomos right now, but you can look it up).
But if you don’t follow that, then you shouldn’t.
I’ve also heard people hold you can shave on friday when it is also rosh chodesh. And I also don’t have time to look that up. But I don’t think I’ve heard of friday which is erev rosh chodesh. But you can look that up.