We well understand your sexual need even when your wife is pregnant.
During the first three months, the pregnant woman is likely to feel exhausted, nauseated and just not in the mood. You must have heard of morning sickness. The breasts often become tender and sore and the size increases. Threatened miscarriage due to orgasms are also possible.
Did you both talk about pregnancy before she became pregnant? Often, a woman is in a state of shock, when it happens. This is her first pregnancy, remember.
Tell me, if you had some mental worry or even a physical strain, would you be in the mood for sex?
Usually, in the next three months she will feel less nauseous, and as there is a build-up of estrogen, her sex drive will also improve. The vagina is more lubricated and the clitoris becomes engorged. Do not insist on sex. Build more of a physical bond by cuddling and kissing. Try to convince her that sex, even when she is pregnant is safe, though advice of her doctor should be taken.
In many women, the opposite is also true. Their libido and sex drive increases when they are pregnant. But each person is different.
You have asked whether you should have paid sex. Would you recommend that to your wife, if you had an accident and were not able to have sex for some time. I read one comment here, telling you that you should have extra-marital sex. Do you want to destroy your marriage? Sex and pregnancy is not the end of marriage. Act wisely, not foolishly. You have your whole life to have sex with your wife.
Be patient with her. Talk to her. Explain to her about your needs for having sex or at least an outlet like masturbating you or a blowjob.