'I have received' is the correct meaning. It would mean that you were either sunburnt, or too hot. Despite Hilary's comment, I would say that it IS something that people say, whether or not it is correct.

We wouldn't say 'I've got too much sun". We might say "I've had too much sun", meaning, I have been exposed to too much sun (and as a result, have sunburn). So yes, this is equivalent in meaning to "I have received (been exposed to) too much sun).