If you are saying “I had two meetings today” then you can say “我今天开了两个会（议）。” If you are saying “I’m going to having two meetings to attend today” , you need to say “我今天要开两个会（议）。”

The tense should be expressed to make it more like human being's speech. So, I would say "我今天开了两个会，快累死了。" (I attended to two meetings today, and I am exhausted.) "我今天有俩会(要开)。" (I have two meetings to attend to today.) Ps. Not like English, "我今天有俩会（I have two meetings）" expresses well enough the meaning of "I have wo meeting [to attend]". to attend to a meeting = 开会，开=attend to, 会=meeting 两会 is a proper noun

As is answered above，“两会”is a proper noun，which means “the two sessions”, viz. "the NPC and CPPCC annual sessions". If you want to say "I had two meetings today." It should be "今天我开了两个会议。“ Notice that”了“ is the symbol of simple past tense in Chinese. If you want to say "I have two meetings to attend today." or "I will have two meetings today." It should be "我今天要开两个会议。“ or “今天我有两个会议要开。”Notice that”要“here means”will“. All in all, the two sentences you offered don't show tense, which is very important in language learning. The meaning can be very different with different tenses. Hope this is helpful.

“两会” is a proper noun in Chinese. If you want to represent two meetings,you can say"两个会议"

Technically, yes. But I’d prefer to say “今天，我开了两会议”