Support staff should not be covering your classes if that is not part of their normal duties.
Do you have a rep in school? They need to speak to your head about this, and remind them of the NAHT (assuming primary?) advice etc to heads. You also need to speak to support staff and remind them they can refuse to cover/refuse to cross the picket line and so on. Do you currently picket your school?
If you don't have a rep in school and don't have the confidence to approach your head directly, then contact your local branch, and they can send in an officer to speak to the head and negotiate on your behalf.
The other thing is to try and encourage other teachers to join the strike. It would be very embarrassing for the head if they said the school would be open, and then had to send students home because now 2 or 3 more teachers were striking and cover hadn't been arranged. If you can create some uncertainty, it makes it harder for the head to plan.
Would other teachers be open to coming to a meeting if your local branch sent in someone to talk to them etc?
I can understand why this is super frustrating, but I don't think the answer is to give up, the answer is to fight more strongly!
You can also have an impact by joining actions in your local area, and engaging with parents etc.