Hi there,
The range of problems you describe suggest to me a complete physical examination would be a good step. You've probably had many appointments but I wonder if they have gone through the whole normal testing process.
A good doctor should do that anyway if you've had depression for a while, test by test often as they eliminate causes.
So that would be first.
If you are depressed I can assure you that you are likely also feeling anxiety. To me anxiety comes first and depressiond evelops from that and remains as the main instigator. It can take many forms. Lying there thinking about all the things that are wrong with you will porvoke anxiety without question and that could be the culprit for elevated heart rate.
Normally though faster heart rates are confined to short periods, during and anxiety attack, during a scare, such as loud noise nearby and so on. Often it can only be for seconds but an anxiety attack can make it last much longer.
You have though been given a diagnosis of this problem by a doctor. Only you deny having anxiety. Both replies here see anxiety in what you write and no doubt the doc did as well. Why not believe it? And try to deal with the anxiety. Firstly by accepting it and then by treating it.
By the by a week without a shower is nothing compared to me. I won't claim an actual record but if I could shower once a week I would be thrilled. I too see no point and use it as a reason to not go out as well. Cunning us depressed people aren't we?
You can suffer from anxiety and not feel as though you have it. I feel this is the cause of your fast heart rate. You are definitely depressed, and I hope you get help with this.