Welcome to the forum!
You are correct about your Swiss citizenship. Because of billateral agreement, Swiss nationals enjoy full EU citizen status within EU, including freedom of movement and labour.There are no immigration formalities to go through - just present your Swiss passport on entry.
If RN means registered nurse, and your qualification is from US, you need to have it verified by the Nursing and Midwifery Council and register as a qualified nurse, under various categories - adult, mental health, pediatric etc. Depending on your Band (registered nurse at Band 5, specialist nurse at Band 6, advanved nurse at Ban7 and matron/nurse consultant at Band 8a to 8c), your pay will vary from £20710 to £26839 for Band 5, depending on pay points (usually awarded according to experience and responsibility). If your monthly gross pay is £1700, you wiill be at the bottom scale of Band 5. Your take-home pay, after deductions, will be around £1350, without pension contributions. At that level you will really struggle to make ends meet with a child (how old?) - you will probably get some extra help from the government in the form of Child Tax Credit and Working Tax Credit. A typical decent two-bedroom flat in Bristol outside the most expensive area like Clifton will be around £550 to £650 a month in rent. On top of that, you will have Council Tax (maybe around £70-£80 a month after discount for a single adult household), utilities around £70 - £100 a month (electricity, gas, water; you can pay monthly, quarterly or by pre-payment meter) and contents insurance around £20. Running a car, after you've paid for it, can be expensive. Insurance maybe £200-£300 a year (with full no claim bonus; will be more with a foreign licence and no UK driving record), tax around £100 to £150 a year, servicing and repairs around £200-£300. Fuel, at around £1.10 a litre for petrol or diesel, will come to around £1000 - £1200 a year for 10000 miles. Food bill can vary hugely, depending on your taste and preference, but allow around £300 a month to include some meals out and moderate alcohol intake. So you can see it will be really tight, with little left for other shopping, entertainment or holidays. It will be a bit better with £1700 net, but you still need to budget carefully.