You should have received a W-2. If not, you can attach a copy of your pay stub(s) showing the withholding from your pay. Also attach a statement that you did not receive a W-2 and this your proof of the withholding that should be credited to you. If you have a paystub that shows the year-to-date accumulated withholding that's the only one you need to include. Be sure to include the name, address and if you know it, the SSN of whoever paid you. This should work Lots of people have trouble getting their W-2s. Everyone should keep their paystubs until you get your ,W-2s, and double check for accuracy. Also, since employers send their W-2s to Social Security (NOT the IRS....surprise), eventually make sure that SS sees your tax return, including paystub so you get credit for your future benefits from SS and Medicare. Now if the cash payments didn't even come with a paystub how do you even know the taxes were withheld? You need to have a talk with the person who is doing the paying so you don't get tangled up in a financial quandry.
If you must, and the family member doesn't provide you with documentation of some kind (the W-2 is the most appropriate, unless they're paying you as "non-employee compensation" on a 1099-Misc and contributing towards your self-employment taxes - which is permissible - see below*), report your income to the best of your ability. If the family member has NOT paid the appropriate state and federal taxes to the correct agencies, s/he will be the one in the most trouble.
* Publication 15-A specifies: "Pub 15-A, under the Statutory Non-Employee definitions: "Companion sitters. Companion sitters are individuals who furnish personal attendance, companionship, or household care services to children or to individuals who are elderly or disabled ... Companion sitters who are not employees of a companion sitting placement service are generally treated as self-employed for all federal tax purposes" and so far as I can tell, they CAN pay the self-employment taxes, but must report it as additional income
* Publication 15-A specifies: "Pub 15-A, under the Statutory Non-Employee definitions: "Companion sitters. Companion sitters are individuals who furnish personal attendance, companionship, or household care services to children or to individuals who are elderly or disabled ... Companion sitters who are not employees of a companion sitting placement service are generally treated as self-employed for all federal tax purposes" and so far as I can tell, they CAN pay the self-employment taxes, but must report it as additional income