You are asking 2 questions.
is it obligatory for me to give Zakat from the profit of the investments?
If the investment is in your bank account, then the majority of scholars say that you need to pay Zakat on it. If, however, the investment is not in your hands (say 401k, ROTH IRA, etc..) then you don't have to pay Zakat until you actually get the money and the money stays with you for a year. More on this answer can be found on question like this:
Zakat on State Pension Account value
However, in my opinion, if you think that you have a large sum of money (for example $20,000) and you are afraid paying Zakah on it will deplete the money faster when you don't have a job, you can do the following:
- Set a separate account and pay the Zakah to that account.
- Once the account is depleted, you can use that Zakah money on yourself and family. If by that time you already have another job you can easily send that money to Zakah organization.
This opinion comes from the same reasoning many scholars say you are allowed to pay Zakah in advance for 1/2 years. I look at it the same way from the other side. In the future once you have a job, you should also consider paying Zakah in advance to avoid issues like this.
It is also mentionable that my wife owns gold jewelery which had been gifted by me and her family
Your second question about the Gold, it is disputed, some scholars say you need to pay Zakah on the entire Gold, some others would say only that your wife doesn't wear. Similar question can be found here:
Is a woman's jewellery subject to zakat?