Most of the noise likely gets in through cracks around the door so a draft stopper and then maybe hanging a blanket over the doorway to cover the other cracks will help.

If there are vents running throughout the house that carry noise then closing/covering the vents when you need silence will help.

If a lot of noise is still getting in even after covering the door and vents, try to figure out which wall it is coming from and rearrange your furniture so that your desk or bed (wherever you need silence) is as far from that wall as possible, then put a layer of stuff against that wall, e.g., bookcases, hang thick blankets, etc.

If the noise is coming from below, thick carpets help.

If the noise is coming from above, although you can't affix anything to the ceiling you can make a little structure around your bed or desk, e.g., two cheap bookcases on either side with a piece of plywood across the top, then fill the gap between the plywood with packaging foam, cushions, pillows, folded blankets, whatever you can get free/cheap. I used the bookcases-and-plywood fort method when I lived below a stomper and it helped a LOT.

You can cover up residual noise with a colored noise generator. Different colors/pitches of noise are better at covering up different outside sounds, e.g., I've personally found brown noise to be better for traffic and white noise to be better for conversation, so experiment and see which works best for blocking out your family.

There are also earplugs and noise cancelling headphones but those can become painful to wear for too many hours in a row.

Googling home recording studio DIY soundproofing tips will get you a lot more ideas of different things to try.