Both the simple past and the past perfect work just fine for the first verb, but "forgot" should be in the simple past in the construction you give.
"Maybe I've forgotten" indicates that you aren't sure whether or not you have forgotten - but what you're actually not sure of is why the listener does not have your phone number, and you are presenting a hypothetical situation that would lead to that happening. Accordingly "maybe I forgot" is best here.
If you really want to use the perfect, you can absolutely do so - but it would be used as "I may/might have forgotten". Here "forget" is clearly in the hypothetical.
As for the rest of your sentence:
First, "sorry" usually takes "be" as its verb: It's either "I feel bad" or "I am sorry". "I feel sorry" is very strong sounding - and typically is only used in the construction "I feel sorry for you" - as in "I do not envy you".
Secondly, you do need to include a direct object for the verb "give" as it is a compulsory ditransitive verb.
And so we end up with:
First, I'm sorry because I thought I had given you our phone number, but I may have forgotten. Anyway, here it is.