Hi Mate_23! Welcome to BB and congrats on finishing your degree!
I don't think you are setting yourself up for failure if you want to go travelling by yourself, however it may be wise to start with a smaller trip first, even just a week-long one in a neighbouring capital city. The key to battling anxiety whilst on holidays is being prepared - plan for as much as you can; where you're staying, where you're going - make a timetable.
I also highly recommend taking a few things that will help calm you if you do have an anxious night - perhaps your favourite novel, a couple of DVDs you like, a diary (that's a MUST) and even your favourite pair of socks. Things that you like and calm you. When I went travelling overseas, I made sure I had my drawing pad and pencils with me, a diary, and some DVDs of comedies I like. And I am glad I took them because there were a couple of nights I felt down in the dumps, and I was able to keep myself stable and finish my holiday.
Keep yourself distracted and busy, take some deep breathes when you need to, and look after yourself. The best part about travelling on your own is the freedom to do what you like, so if you do wake up one morning feeling stressed and anxious, stay in bed, and do what you need to do to get back to a stable state of mind.
I hope other people have some more helpful suggestions. Hopefully you'll be too busy exploring and having fun on your holiday that you'll forget the worries back home. At the end of the day, it doesn't matter if you embarrass yourself on holidays, because you'll never see those people again! (Plus we're all human, we all have those moments)
Read up on the resources for anxiety here on BB, and you can get them sent out to you in the mail for free as well, which I'd recommend you take on your holiday.
Good luck and stay positive!