If I accept Yeshua, won't I have to worship three gods—as do Christians?

Not at all. Actually, Christianity teaches that there is just one G-d—the creator of the universe. In fact, when Yeshua was asked what the greatest commandment was (see Mark 12:28-30), he quoted the Shema (see Deuteronomy 6:4, "Hear, oh Israel, the L-rd our G-d is one L-rd").

However, this one G-d is a compound unity, as hinted at in the Shema. The Hebrew language has two words that can be translated "one": echad and yachid. Whereas yachid refers to the number one (i.e., absolute unity), echad refers to a composite unity. An example of this is in the book of Genesis chapter 2, verse 24, where it says that a couple joined together in marriage shall become one flesh. Since the Shema uses the word echad, not yachid, it is reasonable to say that G-d's essence, or nature, is that of a composite unity. Additional information can be found in the book "A Way in the Wilderness".