Welcome to the forum !
False heats can and do happen of course although when they do it is usually a sign of something wrong somewhere. She could be 'cystic' [Ovarian or follicular] or else have a uterine infection amongst a few of the possibilities.
However, with infection you would see signs of a discharge that sort of thing.
Do you have a bull or other cow at all, some cows present with false heats when kept on their own, in such cases it's more of a mental state than physical.
Do you know how to do a rectal examination ? These are quite easy to do and can be so useful, might be worth you going on an AI course to give you the confidence.
There's not a lot more I can say without seeing your girl for myself sorry.
Hobby farmers or not there may come a time when you really do need a vet, if this is completely outside your financial status you really do need to reconsider your future.
When you take on a cow, or any livestock for that matter you have a responsibility to ensure that they are cared for to the best of your ability and that means that sometimes they will need a vet or other form of treatment, if this is beyond you I urge you to think again.