Your company isn't following standard agile practices.
The developers should be the one estimating, in whatever units you use (hours or Story Points or something else). If you are doing the work, you should be involved in estimating it. In fact, everyone who is required to complete the Story needs to be involved in estimating to make sure that the size is appropriate for the estimated amount of work.
As someone who worked for a contractor, I do understand the need for tracking time. Typically, a Story that is worth more Story Points will take longer to complete due to the various factors. However, there isn't a direct relationship between Story Points and hours. You should look at logging time against a project or activity, not necessarily a particular Story.
In order toTo fix these problems, you should first work on getting realistic estimates in place and using those estimates, along with historical data from previous Sprints, to plan future Sprints. The next step is to look at the overall process to make sure that the Development Team is able to commit to a reasonable amount of work for a Sprint and that, if the work is completed ahead of schedule, that additional work can be brought in. Finally, your Sprint Retrospectives should be used to talk about these problems and come up with methods to fix them.