I have a lot of sympathy with you here, and I imagine a lot of others will too. Nowadays it is extremely difficult to separate fact and fiction from online sources, and to weigh up the relative weight of contrary points that you're being told or are reading about. The reaction of your family clearly isn't helpful. Unfortunately a lot of people who support vaccination and/or are willing to get vaccinated (which is the vast majority of people) are often unable to tell the difference between someone who is anti-vaccination, someone who has legitimate questions surrounding the vaccine, and someone who is caught in the middle, doesn't really know what to think and, as you've said yourself, is scared of what the vaccine is or what taking it may entail. You fall into the latter category but your family seem to be reacting as if you're in the first, which is a common issue.
First of all, we need to deal with the concerns that have no evidential basis at all. There are quite a lot of these and most amount to conspiracy theories. On your journey through some of the wilder corners of the internet you may have read about theories about vaccines being used to control a population by way of implanting tracking or similar devices, or even to cull parts of a population. All of that is nonsense that you can probably recognise, but there are other concerns that you also absolutely do not need to worry about. Fertility is one of those. There is absolutely no evidence that the vaccines affect fertility in any way. It is a myth. The NHS website confirms that (
click here) and there are also articles explaining where the myth originated from (
such as this one). So you do not need to be worried about fertility at all.
The blood clot issue is different, because that is an actual risk, but one that you need to put into context. There have been cases of blood clots associated with Covid-19 vaccines. However, there are two points to note. The first is that that risk is extremely small. To give context, the risk of a woman developing a blood clot from taking the contraceptive pill is about 100 times higher than someone developing a blood clot from the Covid-19 vaccine (as confirmed in the British Medical Journal
here). Generally speaking women don't refuse to take the pill due to risk of blood clots, and broadly speaking the risk is therefore not high enough as a matter of logic to warrant not taking the vaccine.
The second point is that you actually have much more of a chance of developing a blood clot as a result of catching Covid-19 than you do from taking the vaccine (figures vary, but the risk seems to be around 8 to 10 times higher). Still a small chance in the grand scheme of things, but then the more overarching point is that there is a wide range of potential longer term symptoms as a result of catching Covid-19, even if the initial symptoms are not significant. Long Covid is certainly a thing but not fully understood. There is, however, clear anecdotal evidence of a lot of people suffering from longer term effects after catching Covid-19. Those risks, on any reading, seem to be much higher than the very, very small risk of adverse effects from the vaccine.
As a final point, I understand not trusting the government. But there is a difference between not trusting the government to make competent decisions, and not trusting them because you think there's some ulterior motive to them wanting everyone to be vaccinated. The former is a legitimate concern, but one that in this case can be allayed by the actions of other governments and the extensive independent research on Covid-19 vaccines. The latter is a conspiracy theory.
Ultimately it is entirely your decision as to whether or not you do decide to get the vaccine. My own view is that people should for two main reasons. The first is that, at this stage at least, the risks associated with catching Covid-19 (looking primarily at long Covid at this stage) seem to be much higher than those associated with the vaccine. The second is social responsibility, that is to say that irrespective of my own risk of adverse effects if I catch Covid-19, a large proportion of the population need to take the vaccine in order to reduce the risk to the smaller and more vulnerable proportion of the population, and ultimately to bring the country out of the pandemic. But that is just my view. Even if it is the majority view, it's still down to you to make your own choice.