Does tinea versicolor mean my immune system is really bad? does this make me prone to getting infections easier? will it prevents my body from making antibodies?

No. It is simply a surface infestation of the skin by a specific fungus. Your immune system has little knowledge that they are even there. The immune system is triggered when an invader breaches the surface and enters the deep tissues. The lining of the eye, nose, mouth and digestive tract are absorptive surfaces & these are where the immune system is most often alerted. Injections do also.