Is there a laundrette near your new place? That would solve one of your worries. Other basic things you can look for in charity shops, there might also be an online group called 'Freegle' in your area, where people post things for free. Cooking wise - you could use a camping stove until you find a cooker?

Keep taking your medication, times of big change are very stressful and really not a good time to stop.