Is this cheating?

I imagine there'll only be a few reasons as to why the girl gave the number. Save yourself the hassle of explaining to your girlfriend why she isn't anything to worry about and maybe just delete her from your phone. If it's nothing in terms of business/friendship, just delete her and just move on in life with just you and your girlfriend. I know how innocent messaging can seem, but the girl probably wasn't interested in just friends, similar to what your girlfriend feels now. I hope this helps!

What do you reckon she gave me the number for? I feel bad now for messaging her. I wasn’t trying to entertain her

Does sound a bit suss tbh. Like if I'm not single and a girl gives me/asks for a number that's the point I should make it clear I'm not available if I haven't already. If I've done that then I wouldn't have any issue telling my partner or defending my actions.

I won’t hide my actions I’ve even said she can see my Snapchat etc. but nothing like that generally happened

Did you make it clear to them you weren't single though?
How did your girlfriend become aware of this anyway? Did you volunteer the info or has she looked through your phone or something?

No I didn’t make it clear because she never asked. But she never said anything that gave me a thought of wanting like a relationship. She literally was asking what I was doing at that hotel she never said like do you wanna go for a drink or nothing like that. And yeah she went through my phone and was like who’s this and I just said who it was

A girl gave me her phone number from the hotel I was staying at. And I messaged her. It was just generally chit chat absolutely nothing inappropriate. She just asked me what I was doing at the hotel and was telling me about what was in the area etc. but my gf isn’t happy with me but I didn’t ever delete the evidence or nothing. I have told her the truth I can see why she’s annoyed

No I didn’t make it clear because she never asked. But she never said anything that gave me a thought of wanting like a relationship. She literally was asking what I was doing at that hotel she never said like do you wanna go for a drink or nothing like that. And yeah she went through my phone and was like who’s this and I just said who it was

No its not cheating your gf is just being jealous and controlling

Asking to go out for a drink may just be stereotypical. Relationships can spark from anything, anywhere.
Regarding going through phones, it's mostly fine I believe, so long as you aren't doing it regularly and without reason/consent.

Why do you think it's fine to rake through others people correspondence? again, you're not just violating their privacy, but everyone they speak to as they sure as hell haven't gave you consent.
IMO if you're at the point of feeling you need to check someone's phone your relationship is already half over.

A girl gave me her phone number from the hotel I was staying at. And I messaged her. It was just generally chit chat absolutely nothing inappropriate. She just asked me what I was doing at the hotel and was telling me about what was in the area etc. but my gf isn’t happy with me but I didn’t ever delete the evidence or nothing. I have told her the truth I can see why she’s annoyed

As I said, it depends on what you mean by rake. If you asked, it could be a quick check to see what someone put or a complete deep search into their phone, both have their rights and wrongs in each situation. As for violating other people's privacy, whatever is private between other people is private between the person's phone you're going through. The people you speak to should have mutual trust and understanding in what they do with that information, whether that's private or shared with someone else. Therefore, when you're asking to look through someone else's phone, there's trust between everyone involved with the information being shared.
Of course, it goes without saying, that if you go through someone's phone without consent it does violate everyone's privacy involved, yes

Reverse the situation.
If your GF gave her number to a random bloke in a hotel and started chatting with him, how would you feel?

I agree about the going through it without consent thing, but I think even with consent its a bit iffy as 3rd parties messaging you will often presume privacy and that their message will not essentially be published without their knowledge or ability to object. I also think it's just plain unhealthy tbf, people should have some degree of privacy.
I think it's odd to talk of their being trust between everyone here as going through someone's phone implies a complete lack of trust whether it's regular or wanting to read 1 single text - you're telling your partner you don't believe them so as said, you're already half broke up at that point.