Hi, new and advice needed

I think both options are OK. You could wait until your appointment next week. Should your sugars be high(ish), it is not so bad to wait another week, especially as your two recent readings were only a bit elevated or possibly normal, depending on what you ate. That suggests you're not walking around with dangerously high numbers all the time.
On the other hand, should something be wrong, you can take your results with you to your appointment and get possibble better care sooner if your GP has some results to start with.
Third, if I was pre-diabetic and only got tested once a year, I would probably buy my own meter to keep an eye on things and test once a month or so. If you tested when you feel particularly thirsty or tired you could also see if your sugars are high at that particular moment. If they're not, you know your complaints aren't due to high blood sugar.
Meters are cheap or free, teststrips get expensive when used more often. Someone will be along to tell you which meter has the cheapest strips. I forgot as I'm not in the UK, so different brands.
All the best!

Hello Tricia and welcome! Please bear in mind that my observations come from someone with no medical qualifications and fairly limited experience of diabetes. Others will probably offer better advice.
Firstly your single blood glucose tests are not reliable indicators, as very much depends on what you'd eaten and the time between eating and testing as well as any exercise or activity before testing. The primary test for diabetes is a HbA1c test that measures average BG over the previous couple of months. You don't say if your GP has done this.
Secondly, given your symptoms I think you need to discuss these with your GP as they may be indicative of a range of conditions and further tests may be required.
Thirdly, monitoring your own BG may be a good idea, but you need to do it regularly before and after main meals as the results will then start to show how your body is responding to what you eat and its reaction and ability to cope with sugars/carbs.

I'm afraid I can't suggest a meter, I was provided with one by the NHS, but I'm sure others on here will soon pop up with suggestions.

EDIT - just noticed your update and readings were fasting BG which I assume is early morning in which case they are not too bad in my opinion.

Wishing you all the best.

Dave

If you do decide to get a meter, I bought an SD Code Free, it was about £12. The test strips are one of the cheapest.
Here’s the website for them:
https://homehealth-uk.com/product-category/blood-glucose/
If you do order from here, there are discount codes for buying strips in bulk:
5 packs 264086
10 packs 975833